Julián Fernández Bonder

A Nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding

In this paper we study the Sobolev trace embedding

Blow-up vs. spurious steady solutions

W^{1,p}(\Omega)\hookrightarrow L^p_V(\partial \Omega)

Multiple positive solutions for quasilinear elliptic problems with sign-changing nonlinearities

, where

On the Existence of Extremals for the Sobolev Trace Embedding Theorem with Critical Exponent

V

Asymptotic behavior of the eigenvalues of the one-dimensional weighted p-Laplace operator

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

Regularity of the Free Boundary in an Optimization Problem Related to the Best Sobolev Trace Constant

\lambda_k\nearrow +\infty

Uniform Bounds for the Best Sobolev Trace Constant

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 study of the second eigenvalue proving that it coincides with the second variational eigenvalue. --------------------------------------------------------------------------------

AN OPTIMIZATION PROBLEM FOR THE FIRST WEIGHTED EIGENVALUE PROBLEM PLUS A POTENTIAL

In this paper, we study the blow-up problem for positive solutions of a semidiscretization in space of the heat equation in one space dimension with a nonlinear flux boundary condition and a nonlinear absorption term in the equation. We obtain that, for a certain range of parameters, the continuous problem has blow-up solutions but the semidiscretization does not and the reason for this is that a spurious attractive steady solution appears.

Multiple solutions for the p-Laplace operator with critical growth

Using variational arguments, we prove some nonexistence and multiplicity results for positive solutions of a system of p-Laplace equations of gradient form. Then we study a p-Laplace-type problem with nonlinear boundary conditions.

Time-space white noise eliminates global solutions in reaction-diffusion equations

In this paper, the existence problem is studied for extremals of the Sobolev trace inequality W 1,p (Ω) → L p∗ (∂Ω), where Ω is a bounded smooth domain in R N , p∗ = p(N − 1)/(N − p )i s the critical Sobolev exponent, and 1