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• Nonhomogeneous Dirichlet problems without the Ambrosetti-Rabinowitz condition
Li, Gang, matematik ...
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.
Vir: Topological Methods in Nonlinear Analysis. - ISSN 1230-3429 (Vol. 51, no. 1, March 2018, str. 55-77)
Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
Leto - 2018
Jezik - angleški
COBISS.SI-ID - 18162521
vir: Topological Methods in Nonlinear Analysis. - ISSN 1230-3429 (Vol. 51, no. 1, March 2018, str. 55-77)