The Method of Subsuper Solutions for Weighted p(r)-Laplacian Equation Boundary Value Problems.

The article examines the existence of solutions for weighted p(x)-Laplacian ordinary boundary value problem. The method used in this study is based on Leray-Schauder degree. As an application, the existence of weak solutions for p(x)-Laplacian partial differential equations is given. On the p(x)-Laplacian problems, there is a possibility that it does not have the first eigenvalue and the first eigenfunction. Several sub-super-solution theorems for the existence of solutions for weighted p(x)-Laplacian equation with Dirichlet, Robin, and Periodic boundary value conditions are established.