Existence of strong solutions for a class of nonlinear partial differential equations satisfying nonlinear boundary conditions
We give sufficient conditions for the existence of the fundamental solution of a second order evolution equation. The proof is based on stable approximations of an operator A(t) by a sequence of bounded operators.
Existence principles for solutions of singular differential systems satisfying nonlocal boundary conditions are stated. Here is a homeomorphism onto and the Carathéodory function may have singularities in its space variables. Applications of the existence principles are given.
We prove existence results for the Dirichlet problem associated with an elliptic semilinear second-order equation of divergence form. Degeneracy in the ellipticity condition is allowed.
In this paper a fixed point theorem due to Covitz and Nadler for contraction multivalued maps, and the Schaefer’s theorem combined with a selection theorem due to Bressan and Colombo for lower semicontinuous multivalued operators with decomposables values, are used to investigate the existence of solutions for boundary value problems of fourth-order differential inclusions.