Existence of positive and sign-changing solutions for -Laplace equations with potentials in .
Existence of solutions for a nonlinear discrete system involving the -Laplacian
The existence of solutions for boundary value problems for a nonlinear discrete system involving the -Laplacian is investigated. The approach is based on critical point theory.
Existence of three solutions for a class of (p₁,...,pₙ)-biharmonic systems with Navier boundary conditions
We establish the existence of at least three weak solutions for the (p1,…,pₙ)-biharmonic system ⎧ in Ω, ⎨ ⎩ on ∂Ω, for 1 ≤ i ≤ n. The proof is based on a recent three critical points theorem.
Homogenization of the transport equation describing convection-diffusion processes in a material with fine periodic structure
In the present contribution we discuss mathematical homogenization and numerical solution of the elliptic problem describing convection-diffusion processes in a material with fine periodic structure. Transport processes such as heat conduction or transport of contaminants through porous media are typically associated with convection-diffusion equations. It is well known that the application of the classical Galerkin finite element method is inappropriate in this case since the discrete solution...
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.
Nonlinear boundary value problems involving the extrinsic mean curvature operator
The paper surveys recent results obtained for the existence and multiplicity of radial solutions of Dirichlet problems of the type where is the open ball of center and radius in , and is continuous. Comparison is made with similar results for the Laplacian. Topological and variational methods are used and the case of positive solutions is emphasized. The paper ends with the case of a general domain.
Nontrivial solutions for a class of superquadratic elliptic equations
Using a version of the Local Linking Theorem and the Fountain Theorem, we obtain some existence and multiplicity results for a class of superquadratic elliptic equations.
Nontrivial solutions for a robin problem with a nonlinear term asymptotically linear at and superlinear at .
On quasilinear elliptic equations in .
Přechodem hory k řešení okrajové úlohy
Problemi variazionali non lineari di tipo ellittico
Resonance and strong resonance for semilinear elliptic equations in .
Singular limits for a 4-dimensional semilinear elliptic problem with exponential nonlinearity
Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances
We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrödinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate and an explicit representation of the resonant states, we show that the spectral projection has a semiclassical expansion in integer powers of , and compute its leading term. We use this result to compute the residue of the scattering amplitude at such a resonance. Eventually, we...