Matches in SemOpenAlex for { <https://semopenalex.org/work/W4379087859> ?p ?o ?g. }
Showing items 1 to 69 of
69
with 100 items per page.
- W4379087859 abstract "We study the existence and non-existence of positive solutions for the following class of nonlinear elliptic problems in the hyperbolic space $$ -Delta_{mathbb{B}^N} u-lambda u=a(x)u^{p-1} , + , varepsilon u^{2^*-1} ,;;text{in};mathbb{B}^{N}, quad u in H^{1}{(mathbb{B}^{N})}, $$ where $mathbb{B}^N$ denotes the hyperbolic space, $2<p<2^*:=frac{2N}{N-2}$, if $N geqslant 3; 2<p<+infty$, if $N = 2,;lambda < frac{(N-1)^2}{4}$, and $0< ain L^infty(mathbb{B}^N).$ We first prove the existence of a positive radially symmetric ground-state solution for $a(x) equiv 1.$ Next, we prove that for $a(x) geq 1$, there exists a ground-state solution for $varepsilon$ small. For proof, we employ ``conformal change of metric which allows us to transform the original equation into a singular equation in a ball in $mathbb R^N$. Then by carefully analysing the energy level using blow-up arguments, we prove the existence of a ground-state solution. Finally, the case $a(x) leq 1$ is considered where we first show that there is no ground-state solution, and prove the existence of a it bound-state solution rm (high energy solution) for $varepsilon$ small. We employ variational arguments in the spirit of Bahri-Li to prove the existence of high energy-bound-state solutions in the hyperbolic space." @default.
- W4379087859 created "2023-06-02" @default.
- W4379087859 creator A5032167815 @default.
- W4379087859 creator A5043125270 @default.
- W4379087859 creator A5078795716 @default.
- W4379087859 date "2023-05-31" @default.
- W4379087859 modified "2023-09-24" @default.
- W4379087859 title "On a class of elliptic equations with Critical Perturbations in the hyperbolic space" @default.
- W4379087859 doi "https://doi.org/10.48550/arxiv.2305.19781" @default.
- W4379087859 hasPublicationYear "2023" @default.
- W4379087859 type Work @default.
- W4379087859 citedByCount "0" @default.
- W4379087859 crossrefType "posted-content" @default.
- W4379087859 hasAuthorship W4379087859A5032167815 @default.
- W4379087859 hasAuthorship W4379087859A5043125270 @default.
- W4379087859 hasAuthorship W4379087859A5078795716 @default.
- W4379087859 hasBestOaLocation W43790878591 @default.
- W4379087859 hasConcept C11413529 @default.
- W4379087859 hasConcept C114614502 @default.
- W4379087859 hasConcept C121332964 @default.
- W4379087859 hasConcept C122041747 @default.
- W4379087859 hasConcept C134306372 @default.
- W4379087859 hasConcept C138885662 @default.
- W4379087859 hasConcept C174084160 @default.
- W4379087859 hasConcept C186370098 @default.
- W4379087859 hasConcept C2778113609 @default.
- W4379087859 hasConcept C2778572836 @default.
- W4379087859 hasConcept C33923547 @default.
- W4379087859 hasConcept C37914503 @default.
- W4379087859 hasConcept C41895202 @default.
- W4379087859 hasConcept C48103436 @default.
- W4379087859 hasConcept C62520636 @default.
- W4379087859 hasConcept C69523127 @default.
- W4379087859 hasConcept C77553402 @default.
- W4379087859 hasConcept C83677898 @default.
- W4379087859 hasConceptScore W4379087859C11413529 @default.
- W4379087859 hasConceptScore W4379087859C114614502 @default.
- W4379087859 hasConceptScore W4379087859C121332964 @default.
- W4379087859 hasConceptScore W4379087859C122041747 @default.
- W4379087859 hasConceptScore W4379087859C134306372 @default.
- W4379087859 hasConceptScore W4379087859C138885662 @default.
- W4379087859 hasConceptScore W4379087859C174084160 @default.
- W4379087859 hasConceptScore W4379087859C186370098 @default.
- W4379087859 hasConceptScore W4379087859C2778113609 @default.
- W4379087859 hasConceptScore W4379087859C2778572836 @default.
- W4379087859 hasConceptScore W4379087859C33923547 @default.
- W4379087859 hasConceptScore W4379087859C37914503 @default.
- W4379087859 hasConceptScore W4379087859C41895202 @default.
- W4379087859 hasConceptScore W4379087859C48103436 @default.
- W4379087859 hasConceptScore W4379087859C62520636 @default.
- W4379087859 hasConceptScore W4379087859C69523127 @default.
- W4379087859 hasConceptScore W4379087859C77553402 @default.
- W4379087859 hasConceptScore W4379087859C83677898 @default.
- W4379087859 hasLocation W43790878591 @default.
- W4379087859 hasOpenAccess W4379087859 @default.
- W4379087859 hasPrimaryLocation W43790878591 @default.
- W4379087859 hasRelatedWork W1994181027 @default.
- W4379087859 hasRelatedWork W2065901967 @default.
- W4379087859 hasRelatedWork W2089645279 @default.
- W4379087859 hasRelatedWork W2913693922 @default.
- W4379087859 hasRelatedWork W2948378305 @default.
- W4379087859 hasRelatedWork W2956003067 @default.
- W4379087859 hasRelatedWork W3125364341 @default.
- W4379087859 hasRelatedWork W4309680666 @default.
- W4379087859 hasRelatedWork W2034525779 @default.
- W4379087859 hasRelatedWork W4221141505 @default.
- W4379087859 isParatext "false" @default.
- W4379087859 isRetracted "false" @default.
- W4379087859 workType "article" @default.