Nonhomogeneous Dirichlet problems without the Ambrosetti-Rabinowitz condition

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

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.

• Jezik: Angleški jezik
• Ključne besede: nonhomogeneous differential operator, Ambrosetti-Rabinowitz condition, Cerami compactness condition, Sobolev space with variable exponent
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2018
• Št. strani: Str. 55-77
• Številčenje: Vol. 51, no. 1
• PID: 20.500.12556/RUL-109292
• UDK: 517.956.2
• ISSN pri članku: 1230-3429
• DOI: 10.12775/TMNA.2017.037
• COBISS.SI-ID: 18162521
• Datum objave v RUL: 29.08.2019

Gradivo je del revije

• Naslov: Topological Methods in Nonlinear Analysis
• Skrajšan naslov: Topol. Methods Nonlinear Anal.
• Založnik: Juliusz Schauder Center for Nonlinear Studies
• ISSN: 1230-3429
• COBISS.SI-ID: 14203653