The symmetry of minimizing harmonic maps from a two dimensional domain to the sphere
The use of Cerami sequences in critical point theory.
Three non-trival solutions of anticoercive boundary value problems for the Pseudo-Laplace-operator.
Three solutions for a nonlinear Neumann boundary value problem
The aim of this paper is to establish the existence of at least three solutions for the nonlinear Neumann boundary-value problem involving the p(x)-Laplacian of the form in Ω, on ∂Ω. Our technical approach is based on the three critical points theorem due to Ricceri.
Three solutions for quasilinear equations in near resonance.
Three solutions for singular -Laplacian type equations.
Topological sectors for Ginzburg-Landau energies.
Towards a two-scale calculus
We define and characterize weak and strong two-scale convergence in Lp, C0 and other spaces via a transformation of variable, extending Nguetseng's definition. We derive several properties, including weak and strong two-scale compactness; in particular we prove two-scale versions of theorems of Ascoli-Arzelà, Chacon, Riesz, and Vitali. We then approximate two-scale derivatives, and define two-scale convergence in spaces of either weakly or strongly differentiable functions. We also derive...
Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity: some results and open problems
This text is a survey of recent results on traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity. We present the existence, nonexistence and stability results and we describe the main ideas used in proofs.
Traveling waves in a cylinder rolling on a flat surface
Trudinger–Moser inequality on the whole plane with the exact growth condition
Trudinger-Moser inequality is a substitute to the (forbidden) critical Sobolev embedding, namely the case where the scaling corresponds to . It is well known that the original form of the inequality with the sharp exponent (proved by Moser) fails on the whole plane, but a few modied versions are available. We prove a precised version of the latter, giving necessary and sufficient conditions for the boundedness, as well as for the compactness, in terms of the growth and decay of the nonlinear function....
Two constant sign solutions for a nonhomogeneous Neumann boundary value problem
We consider a nonlinear Neumann problem with a nonhomogeneous elliptic differential operator. With some natural conditions for its structure and some general assumptions on the growth of the reaction term we prove that the problem has two nontrivial solutions of constant sign. In the proof we use variational methods with truncation and minimization techniques.
Two Dimensional Variational Problems with Thin Obstacles.
Two functionals for which minimizers are also minimizers.
Two-scale div-curl lemma
The div-curl lemma, one of the basic results of the theory of compensated compactness of Murat and Tartar, does not take over to the case in which the two factors two-scale converge in the sense of Nguetseng. A suitable modification of the differential operators however allows for this extension. The argument follows the lines of a well-known paper of F. Murat of 1978, and uses a two-scale extension of the Fourier transform. This result is also extended to time-dependent functions, and is applied...