Gang Li (Avtor), Vicenţiu Rǎdulescu (Avtor), Dušan Repovš (Avtor), Qihu Zhang (Avtor)

Povzetek

We consider the existence of solutions of the following ▫$p(x)$▫-Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition: ▫$$ \begin{cases} -\text{div} \, (|\nabla u|^{p(x)-2}\nabla u) = f(x,u) & \text{ in } \quad \Omega , \\ u=0 & \text{ on } \quad \partial \Omega . \end{cases} $$▫ We give a new growth condition and we point out its importance for checking the Cerami compactness condition. We prove the existence of solutions of the above problem via the critical point theory, and also provide some multiplicity properties. The present paper extend previous results of Q. Zhang and C. Zhao (Existence of strong solutions of a ▫$p(x)$▫-Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition, Computers and Mathematics with Applications, 2015) and we establish the existence of solutions under weaker hypotheses on the nonlinear term.

Ključne besede

nonhomogeneous differential operator;Ambrosetti-Rabinowitz condition;Cerami compactness condition;Sobolev space with variable exponent;

Podatki

Jezik: Angleški jezik
Leto izida:
Tipologija: 1.01 - Izvirni znanstveni članek
Organizacija: UL FMF - Fakulteta za matematiko in fiziko
UDK: 517.956.2
COBISS: 18162521 Povezava se bo odprla v novem oknu
ISSN: 1230-3429
Št. ogledov: 589
Št. prenosov: 380
Ocena: 0 (0 glasov)
Metapodatki: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Ostali podatki

Vrsta dela (COBISS): Članek v reviji
Strani: str. 55-77
Letnik: ǂVol. ǂ51
Zvezek: ǂno. ǂ1
Čas izdaje: March 2018
DOI: 10.12775/TMNA.2017.037
ID: 11210456