A minimax formula for the principal eigenvalues of Dirichlet problems and its applications.
A minimax principle, index of the critical point, and existence of sign-changing solutions to elliptic boundary value problems.
A minimization problem arising from prescribing scalar curvature functions.
A mixed finite element method close to the equilibrium model applied to plane elastostatics
A multiplicity result for quasilinear problems with convex and concave nonlinearities and nonlinear boundary conditions inunbounded domains.
A multiplicity theorem for the Neumann problem for nonlinear hemivariational inequalities
A new approach to Young measure theory, relaxation and convergence in energy
A new type of solutions for a singularly perturbed elliptic Neumann problem.
A nonexistence result for a nonlinear equation involving critical Sobolev exponent
A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.
In this paper we study the Sobolev trace embedding W1,p(Ω) → LpV (∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λk / +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end this article with the...
A nontrivial solution for Neumann noncoercive hemivariational inequalities
In this paper we consider Neumann noncoercive hemivariational inequalities, focusing on nontrivial solutions. We use the critical point theory for locally Lipschitz functionals.
A note on a critical problem with natural growth in the gradient
The paper analyzes the influence on the meaning of natural growth in the gradient of a perturbation by a Hardy potential in some elliptic equations. Indeed, in the case of the Laplacian the natural problem becomes in , on , . This problem is a particular case of problem (2). Notice that is optimal as coefficient and exponent on the right hand side.
A note on bounds for non-linear multivalued homogenized operators
In this paper we study the behaviour of maximal monotone multivalued highly oscillatory operators. We construct Reuss-Voigt-Wiener and Hashin-Shtrikmann type bounds for the minimal sections of G-limits of multivalued operators by using variational convergence and convex analysis.
A note on nodal non-radially symmetric solutions to Emden-Fowler equations.
A note on quasilinear elliptic eigenvalue problems.
A note on the existence of two nontrivial solutions of a resonance problem.
A one-dimensional nonlinear degenerate elliptic equation.
A pattern formation problem on the sphere.
A priori regularity for weak solutions of some nonlinear elliptic equations
A regularity result for a convex functional and bounds for the singular set
In this paper we prove a regularity result for local minimizers of functionals of the Calculus of Variations of the typewhere Ω is a bounded open set in , u∈(Ω; ), p> 1, n≥ 2 and N≥ 1. We use the technique of difference quotient without the usual assumption on the growth of the second derivatives of the function f. We apply this result to give a bound on the Hausdorff dimension of the singular set of minimizers.