Minimax principles for critical-point theory in applications to quasilinear boundary-value problems.
Modified wave operators for nonlinear Schrödinger equations in one and two dimensions.
Multiple critical points of perturbed symmetric strongly indefinite functionals
Multiple solutions for nonlinear discontinuous elliptic problems near resonance
We consider a quasilinear elliptic eigenvalue problem with a discontinuous right hand side. To be able to have an existence theory, we pass to a multivalued problem (elliptic inclusion). Using a variational approach based on the critical point theory for locally Lipschitz functions, we show that we have at least three nontrivial solutions when from the left, being the principal eigenvalue of the p-Laplacian with the Dirichlet boundary conditions.
Multiple solutions of a Schrödinger type semilinear equation
Two nontrivial solutions are obtained for nonhomogeneous semilinear Schrödinger equations.
Multiplicity of positive solutions for second order quasilinear equations
We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.
Multiplicity of positive solutions to semilinear elliptic boundary value problems.