Multiple positive solutions for quasilinear elliptic problems with sign-changing nonlinearities.
Infinitely many solutions for an elliptic system with nonlinear boundary conditions.
Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions.
Multiple solutions for the -Laplace equation with nonlinear boundary conditions.
Concentration-compactness principle for variable exponent spaces and applications.
Asymptotic behaviour for a parabolic system with nonlinear boundary conditions.
A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.
In this paper we study the Sobolev trace embedding W(Ω) → L (∂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 λ / +∞ 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...
Simultaneous vs. non-simultaneous blow-up in numerical approximations of a parabolic system with non-linear boundary conditions
We study the asymptotic behavior of a semi-discrete numerical approximation for a pair of heat equations , in ; fully coupled by the boundary conditions , on , where is a bounded smooth domain in . We focus in the existence or not of non-simultaneous blow-up for a semi-discrete approximation . We prove that if blows up in finite time then can fail to blow up if and only if and , which is the same condition as the one for non-simultaneous blow-up in the continuous problem. Moreover,...
Symmetry properties for the extremals of the Sobolev trace embedding
Simultaneous non-simultaneous blow-up in numerical approximations of a parabolic system with non-linear boundary conditions
We study the asymptotic behavior of a semi-discrete numerical approximation for a pair of heat equations , in Ω x (0,); fully coupled by the boundary conditions , on ∂Ω x (0,), where is a bounded smooth domain in . We focus in the existence or not of non-simultaneous blow-up for a semi-discrete approximation . We prove that if blows up in finite time then can fail to blow up if and only if > 1 and < 2( - 1) , which is the same...
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