Subcritical perturbations of resonant linear problems with sign-changing potential.
Supercritical elliptic problems in domains with small holes
Superlinear equations and a uniform anti-maximum principle for the multi-Laplacian operator.
Superlinear equations involving nonlinearities limited by asymptotically homogeneous functions.
Symmetry and concentration behavior of ground state in axially symmetric domains.
Symmetry and monotonicity of solutions to some variational problems in cylinders and annuli.
The eigenvalue problem for a singular quasilinear elliptic equation.
The existence and uniqueness of solution of Duffing equations with non- perturbation functional at nonresonance.
The existence of positive solution to some asymptotically linear elliptic equations in exterior domains.
In this paper, we are concerned with the asymptotically linear elliptic problem -Δu + λ0u = f(u), u ∈ H01(Ω) in an exterior domain Ω = RnO (N ≥ 3) with O a smooth bounded and star-shaped open set, and limt→+∞ f(t)/t = l, 0 < l < +∞. Using a precise deformation lemma and algebraic topology argument, we prove under our assumptions that the problem possesses at least one positive solution.
The -Laplace eigenvalue problem as in a Finsler metric
We consider the -Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite and investigate the limit problem as .
The use of Cerami sequences in critical point theory.
Three nodal solutions of singularly perturbed elliptic equations on domains without topology
Unilateral boundary value problems with jump discontinuities.
Upper bound for the number of eigenvalues for nonlinear operators
Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket
Under an appropriate oscillating behaviour either at zero or at infinity of the nonlinear term, the existence of a sequence of weak solutions for an eigenvalue Dirichlet problem on the Sierpiński gasket is proved. Our approach is based on variational methods and on some analytic and geometrical properties of the Sierpiński fractal. The abstract results are illustrated by explicit examples.
Variational and topological methods for operator equations involving duality mappings on Orlicz-Sobolev spaces.
Variational method to the impulsive equation with Neumann boundary conditions.
Variational methods for a resonant problem with the -Laplacian in .
Variational methods for almost periodic solutions of a class of neutral delay equations.
Weak linking theorems and Schrödinger equations with critical Sobolev exponent
In this paper we establish a variant and generalized weak linking theorem, which contains more delicate result and insures the existence of bounded Palais–Smale sequences of a strongly indefinite functional. The abstract result will be used to study the semilinear Schrödinger equation , where are periodic in for and 0 is in a gap of the spectrum of ; . If for an appropriate constant , we show that this equation has a nontrivial solution.