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The existence of solutions for boundary value problems for a nonlinear discrete system involving the -Laplacian is investigated. The approach is based on critical point theory.
We establish the existence of solutions for evolution equations in Hilbert spaces with anti-periodic boundary conditions. The energies associated to these evolution equations are quadratic forms. Our approach is based on application of the Schaefer fixed-point theorem combined with the continuity method.
We prove existence of weak solutions to doubly degenerate diffusion equations
by Faedo-Galerkin approximation for general domains and general nonlinearities. More precisely, we discuss the equation in an abstract setting, which allows to choose function spaces corresponding to bounded or unbounded domains with Dirichlet or Neumann boundary conditions. The function can be an inhomogeneity or a nonlinearity involving terms of the form or . In the appendix, an introduction to weak differentiability...
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