A nonexistence test for biharmonic Green's functions of clamped bodies.
A nonexistence theorem for an equation with critical Sobolev exponent in the half space.
A nonhomogeneous backward heat problem: regularization and error estimates.
A nonlinear adaptative multiresolution method in finite differences with incremental unknowns
A nonlinear boundary problem involving the -bi-Laplacian operator.
A nonlinear boundary value problem for a system of hyperbolic partial differential equations.
A nonlinear degenerate parabolic equation
A nonlinear diffusion equation with nonlinear boundary conditions: Method of lines
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 nonlinear elliptic boundary value problem
A nonlinear elliptic equation with singular potential and applications to nonlinear field equations
We prove the existence of cylindrical solutions to the semilinear elliptic problem , , , where , and has a double-power behaviour, subcritical at infinity and supercritical near the origin. This result also implies the existence of solitary waves with nonvanishing angular momentum for nonlinear Schr¨odinger and Klein–Gordon equations.
A nonlinear evolution equation modelling the Marangoni effect : existence of solution and numerical methods
A nonlinear evolution inclusion in perfect plasticity with friction.
A nonlinear heat equation with temperature-dependent parameters.
A non-linear hyperbolic equation.
A nonlinear oblique derivative boundary value problem for the heat equation. Part 1 : basic results
A nonlinear oblique derivative boundary value problem for the heat equation : analogy with the porous medium equation
A nonlinear oblique derivative boundary value problem for the heat equation. Part 2 : singular self-similar solutions
A nonlinear operator in potential theory
A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology.
We present some results on the mathematical treatment of a global two-dimensional diffusive climate model. The model is based on a long time averaged energy balance and leads to a nonlinear parabolic equation for the averaged surface temperature. The spatial domain is a compact two-dimensional Riemannian manifold without boundary simulating the Earth. We prove the existence of bounded weak solutions via a fixed point argument. Although, the uniqueness of solutions may fail, in general, we give a...