74 research outputs found
Multiplicity of nontrivial solutions for elliptic equations with nonsmooth potential and resonance at higher eigenvalues
We consider a semilinear elliptic equation with a nonsmooth, locally
\hbox{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.Comment: 23 page
Nodal and constant sign solutions for singular elliptic problems
We establish the existence of multiple solutions for singular quasilinear
elliptic problems with a precise sign information: two opposite constant sign
solutions and a nodal solution. The approach combines sub-supersolutions method
and Leray-Schauder topological degree involving perturbation argument
On the proof of a minimax principle
The aim of this note is to point out that the basic argument in the proof of Theorem 2 in [5] does not work. Comments on this topic are given
Existence of solutions for implicit obstacle problems of fractional laplacian type involving set-valued operators
The paper is devoted to a new kind of implicit obstacle problem given by a fractional Laplacian-type operator and a set-valued term, which is described by a generalized gradient. An existence theorem for the considered implicit obstacle problem is established, using a surjectivity theorem for set-valued mappings, Kluge’s fixed point principle and nonsmooth analysis
Variational-hemivariational inequalities with nonhomogeneous Neumann boundary condition
The aim of this paper is the study of variational-hemivariational inequalities with nonhomogeneous Neumann boundary condition. Sufficient conditions for the existence of a whole sequence of solutions which is either unbounded or converges to zero are proved. For homogeneous Neumann boundary condition, results of this type have been obtained in Marano and Motreanu [3]. Our approach is based on abstract nonsmooth critical point results given in [3]. The applicability of our results is demonstrated by providing two verifiable criteria which address problems with nonsmooth potential and nonzero Neumann boundary condition
On competing (p,q) -Laplacian Drichlet problem with unbounded weight
We investigate the existence of generalized solutions to coercive competing
system driven by the (p,q) -Laplacian with unbounded perturbation corresponding
to the leading term in the differential operator and with convection depending
on the gradient. Some abstract principle leading to the existence of
generalized solutions is also derived basing on the Galerkin scheme
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