Existence of solutions for -Laplacian equations.
We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of , p≥ 3, type. The weight is a positive power of the distance from a distinguished plane. To prove the existence of solutions we use our result on existence in a weighted L₂ space.
We consider the Poisson equation with the Dirichlet and the Neumann boundary conditions in weighted Sobolev spaces. The weight is a positive power of the distance to a distinguished plane. We prove the existence of solutions in a suitably defined weighted space.
This paper presents several sufficient conditions for the existence of weak solutions to general nonlinear elliptic problems of the type where is a bounded domain of , . In particular, we do not require strict monotonicity of the principal part , while the approach is based on the variational method and results of the variable exponent function spaces.
MSC 2010: 44A35, 35L20, 35J05, 35J25In this paper are found explicit solutions of four nonlocal boundary value problems for Laplace, heat and wave equations, with Bitsadze-Samarskii constraints based on non-classical one-dimensional convolutions. In fact, each explicit solution may be considered as a way for effective summation of a solution in the form of nonharmonic Fourier sine-expansion. Each explicit solution, may be used for numerical calculation of the solutions too.