{"id":"https://openalex.org/W7220737906","doi":"https://doi.org/10.48550/arxiv.2610.06326","title":"Solutions stable outside a compact set for anisotropic quasilinear equations with negative exponent or exponential nonlinearity","display_name":"Solutions stable outside a compact set for anisotropic quasilinear equations with negative exponent or exponential nonlinearity","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220737906","doi":"https://doi.org/10.48550/arxiv.2610.06326"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.06326","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06326","pdf_url":"https://arxiv.org/pdf/2610.06326","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.06326","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030791069","display_name":"Nhat Vy Huynh","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huynh, Nhat Vy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045692299","display_name":"Phuong Le","orcid":"https://orcid.org/0000-0003-4724-7118","observed_orcids":["https://orcid.org/0000-0003-4724-7118"]},"institutions":[{"id":"https://openalex.org/I123565023","display_name":"Vietnam National University Ho Chi Minh City","ror":"https://ror.org/00waaqh38","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023"]},{"id":"https://openalex.org/I4387155442","display_name":"University of Economics and Law","ror":"https://ror.org/0138jhg57","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023","https://openalex.org/I4387155442"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Le, Phuong","raw_affiliation_strings":["Faculty of Economic Mathematics , University of Economics and Law , Ho Chi Minh City , Vietnam;","Vietnam National University , Ho Chi Minh City , Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Economic Mathematics , University of Economics and Law , Ho Chi Minh City , Vietnam;","institution_ids":["https://openalex.org/I4387155442"]},{"raw_affiliation_string":"Vietnam National University , Ho Chi Minh City , Vietnam","institution_ids":["https://openalex.org/I123565023"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/exponential-nonlinearity","display_name":"exponential nonlinearity","score":0.996999979019165},{"id":"https://openalex.org/keywords/stability-of-solutions","display_name":"stability of solutions","score":0.5410000085830688},{"id":"https://openalex.org/keywords/nonexistence-of-solutions","display_name":"nonexistence of solutions","score":0.7020000219345093},{"id":"https://openalex.org/keywords/exterior-solutions","display_name":"exterior solutions","score":0.6790000200271606}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7028999924659729},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6614000201225281},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.5232999920845032},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.47749999165534973},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.4706000089645386},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.46549999713897705},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.46219998598098755},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.453000009059906},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.44859999418258667},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.44670000672340393},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.43950000405311584},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.38999998569488525},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.38989999890327454},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.38589999079704285},{"id":"https://openalex.org/C164154869","wikidata":"https://www.wikidata.org/wiki/Q901927","display_name":"Critical exponent","level":3,"score":0.375900000333786},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C2779844894","wikidata":"https://www.wikidata.org/wiki/Q5421516","display_name":"Exponential dichotomy","level":3,"score":0.3118000030517578},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.30709999799728394},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.27410000562667847},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.2628999948501587},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25859999656677246},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2547000050544739}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.06326","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06326","pdf_url":"https://arxiv.org/pdf/2610.06326","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.06326","doi":"https://doi.org/10.48550/arxiv.2610.06326","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.06326","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.06326","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06326","pdf_url":"https://arxiv.org/pdf/2610.06326","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220737906.pdf","grobid_xml":"https://content.openalex.org/works/W7220737906.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7077068840","https://openalex.org/W7220445155"],"related_works":["https://openalex.org/W7119465783","https://openalex.org/W7154146065","https://openalex.org/W4393127383","https://openalex.org/W2000603684","https://openalex.org/W4387436154","https://openalex.org/W3172898918","https://openalex.org/W7083187189","https://openalex.org/W3195249526","https://openalex.org/W3117995522","https://openalex.org/W4378191811"],"abstract_inverted_index":{"We":[0,31,107],"study":[1],"the":[2,19,42,52,58,77,90,115,131,136,155],"equations":[3],"$\u0394_p^H":[4,13,70],"u=u^{-q}$,":[5],"$u>0$,":[6],"and":[7,29,48,56,113,143,158],"$-\u0394_p^H":[8],"u=e^u$":[9],"in":[10,151],"$\\mathbb{R}^N$,":[11],"where":[12,63],"u=\\operatorname{div}(H(\\nabla":[14],"u)^{p-1}\\nabla":[15],"H(\\nabla":[16,125],"u))$":[17,126],"is":[18],"Finsler":[20],"$p$-Laplacian":[21],"associated":[22],"with":[23,99,127,139],"a":[24,38,65],"uniformly":[25],"convex":[26],"norm":[27],"$H$,":[28],"$p\\ge2$.":[30],"prove":[32,109],"nonexistence":[33],"of":[34,69],"solutions":[35],"stable":[36],"outside":[37],"compact":[39],"set":[40],"for":[41,57,82,89,114,121,135,154],"negative-power":[43,116],"equation":[44,60,117],"when":[45,61,111,118],"$p\\le":[46],"N<\\frac{p(p+3)}{p-1}$":[47],"$q$":[49],"lies":[50],"above":[51,74],"sharp":[53],"critical":[54],"threshold,":[55],"exponential":[59,91],"$pq\u03c4$,":[62],"$\u03c4=\\frac{p}{q+p-1}$,":[64],"positive":[66],"exterior":[67],"solution":[68,79],"u=u^{-q}$":[71],"cannot":[72],"remain":[73],"$\u03b8$":[75],"times":[76],"singular":[78],"near":[80],"infinity":[81],"any":[83],"$\u03b8>1$.":[84],"An":[85],"analogous":[86],"obstruction":[87],"holds":[88],"equation.":[92],"Both":[93],"obstructions":[94],"are":[95],"proved":[96],"by":[97],"comparison":[98],"explicit":[100],"radial":[101],"barriers":[102],"having":[103],"frozen":[104],"right-hand":[105],"sides.":[106],"also":[108,148],"sharpness":[110],"$N>p$,":[112],"$N=p>2$.":[119],"Finally,":[120],"operators":[122],"$\\operatorname{div}(B'(H(\\nabla":[123],"u))\\nabla":[124],"$p$-growth,":[128],"we":[129],"establish":[130],"integral":[132],"estimates":[133],"needed":[134],"stability":[137],"arguments":[138,147],"fully":[140],"justified":[141],"truncation":[142],"absorption":[144],"procedures.":[145],"These":[146],"repair":[149],"gaps":[150],"earlier":[152],"proofs":[153],"corresponding":[156],"isotropic":[157],"anisotropic":[159],"problems.":[160]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}