On a class of superlinear nonlocal fractional problems without Ambrosetti–Rabinowitz type conditions

In this note, we deal with the existence of infinitely many solutions for a problem driven by nonlocal integro-differential operators with homogeneous Dirichlet boundary conditions −LKu = λ f(x, u), in Ω, u = 0, in Rn\Ω, where Ω is a smooth bounded domain of Rn and the nonlinear term f satisfies sup...

Full description

Saved in:
Bibliographic Details
Main Author: Zhou Qing-Mei
Format: Serial
Published: 2019
Series:Electronic journal of qualitative theory of differential equations
Kulcsszavak:Integrodifferenciál-egyenlet
doi:10.14232/ejqtde.2019.1.17

Online Access:http://acta.bibl.u-szeged.hu/58100
Description
Summary:In this note, we deal with the existence of infinitely many solutions for a problem driven by nonlocal integro-differential operators with homogeneous Dirichlet boundary conditions −LKu = λ f(x, u), in Ω, u = 0, in Rn\Ω, where Ω is a smooth bounded domain of Rn and the nonlinear term f satisfies superlinear at infinity but does not satisfy the the Ambrosetti–Rabinowitz type condition. The aim is to determine the precise positive interval of λ for which the problem admits at least two nontrivial solutions by using abstract critical point results for an energy functional satisfying the Cerami condition.
Physical Description:1-12
ISSN:1417-3875