Multiplicity of nontrivial solutions for elliptic equations with nonsmooth potential and resonance at higher eigenvalues
Leszek Gasi'nski, Dumitru Motreanu, Nikolaos S Papageorgiou
Abstract
We consider a semilinear elliptic equation with a nonsmooth, locally Lipschitz potential function (hemivariational inequality). Our hypotheses permit double resonance at infinity and at zero (double-double resonance situation). Our approach is based on the nonsmooth critical point theory for locally Lipschitz functionals and uses an abstract multiplicity result under local linking and an extension of the Castro--Lazer--Thews reduction method to a nonsmooth setting, which we develop here using tools from nonsmooth analysis.
Create a lesson
Related papers
Monotonicity of the propagation speed with respect to the diffusion in a Lotka-Volterra competition-diffusion system
Cyrille Kenne
Sign-preserving solutions to the Tzitzéica equation on lattice graphs
Pengxiu Yu, Yiping Zhang
Concavity and other properties of the entropy on manifolds
Xuenan Fu, Juanling Lu, Qi S. Zhang
The Higher-Dimensional Nitsche Conjecture: Sharp Bounds and Rigidity
Bin Deng, Jiahuan Li, Yilu Liu et al.
The complete spectrum of the linearized p-Laplacian at a Sobolev extremal
Yitian Zhang
Rigidity and existence of Busemann profiles for the Allen--Cahn equation on Cartan--Hadamard manifolds
Luis Eduardo Osorio-Acevedo, Álvaro Jaramillo