Multiplicity of nontrivial solutions for elliptic equations with nonsmooth potential and resonance at higher eigenvalues

2006/07/25 by Leszek Gasi'nski, Gasi'nski, Leszek, Dumitru Motreanu +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.math/0607621

23 pages

arxiv created 2006/07/25 · arxiv updated 2009/12/01

Abstract

We consider a semilinear elliptic equation with a nonsmooth, locally \hboxLipschitz 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.

Related

• Multiplicity results for non-local operators of elliptic type
• A nonsmooth variational approach to differential problems. A case study of nonresonance under the first eigenvalue for a strongly nonlinear elliptic problem
• Linear Elliptic equations with nonlinear boundary conditions under strong resonance conditions
• On the solvability of resonance problems for nonlocal elliptic equations
• Multiplicity of solutions for resonant and non-resonant asymptotically linear elliptic problems