A class of --Laplacian type equation with potentials eigenvalue problem in .
A double eigenvalue problem for Schrödinger equations involving sublinear nonlinearities at infinity.
A global bifurcation result of a Neumann problem with indefinite weight.
A global continuation theorem for obtaining eigenvalues and bifurcation points
A maxmin principle for nonlinear eigenvalue problems with application to a rational spectral problem in fluid-solid vibration
In this paper we prove a maxmin principle for nonlinear nonoverdamped eigenvalue problems corresponding to the characterization of Courant, Fischer and Weyl for linear eigenproblems. We apply it to locate eigenvalues of a rational spectral problem in fluid-solid interaction.
A Multiscale Enrichment Procedure for Nonlinear Monotone Operators
In this paper, multiscale finite element methods (MsFEMs) and domain decomposition techniques are developed for a class of nonlinear elliptic problems with high-contrast coefficients. In the process, existing work on linear problems [Y. Efendiev, J. Galvis, R. Lazarov, S. Margenov and J. Ren, Robust two-level domain decomposition preconditioners for high-contrast anisotropic flows in multiscale media. Submitted.; Y. Efendiev, J. Galvis and X. Wu, J. Comput. Phys. 230 (2011) 937–955; J. Galvis and...
A nonlinear adaptative multiresolution method in finite differences with incremental unknowns
A nonlinear boundary problem involving the -bi-Laplacian operator.
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 note on quasilinear elliptic eigenvalue problems.
A one dimensional Hammerstein problem.
A rational spectral problem in fluid-solid vibration.
A result on the bifurcation from the principal eigenvalue of the -Laplacian.
A two parameters Ambrosetti-Prodi problem.
A Variational Approach to Bifurcation in Lp on an Unbounded Symmetrical Domain.
A variational approach to bifurcation into spectral gaps
About Uniqueness for Nonlinear Boundary Value Problems.
𝒞1,β regularity for Dirichlet problems associated to fully nonlinear degenerate elliptic equations
We prove Hölder regularity of the gradient, up to the boundary for solutions of some fully-nonlinear, degenerate elliptic equations, with degeneracy coming from the gradient.
An abstract differential inequality and eigenvalues of variational inequalities
An asymmetric Neumann problem with weights