The boundary value condition of an evolutionary p ( x ) $p(x)$ -Laplacian equation

AN EVOLUTIONARY WEIGHTED p-LAPLACIAN WITH NEUMANN BOUNDARY VALUE CONDITION IN A PERFORATED DOMAIN

In this paper, we study an evolutionary weighted p-Laplacian with Neumann boundary value condition in a perforated domain. We discuss the removability of the orifice for the radially symmetric steady solution, the general steady solution and for the evolutionary solution of the problem considered.

A FREE-BOUNDARY PROBLEM FOR THE EVOLUTION p-LAPLACIAN EQUATION WITH A COMBUSTION BOUNDARY CONDITION

We study the existence, uniqueness and regularity of solutions of the equation ft = ∆pf = div (|Df | p−2 Df) under over-determined boundary conditions f = 0 and |Df | = 1. We show that if the initial data is concave and Lipschitz with a bounded and convex support, then the problem admits a unique solution which exists until it vanishes identically. Furthermore, the free-boundary of the support ...

Existence and multiplicity of solutions to a p-Laplacian equation with nonlinear boundary condition

We study the nonlinear elliptic boundary value problem Au = f(x, u) in Ω , Bu = g(x, u) on ∂Ω , where A is an operator of p−Laplacian type, Ω is an unbounded domain in R with non-compact boundary, and f and g are subcritical nonlinearities. We show existence of a nontrivial nonnegative weak solution when both f and g are superlinear. Also we show existence of at least two nonnegative solutions ...

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

The fibering map approach to a quasilinear degenerate p(x)-Laplacian equation

‎By considering a degenerate $p(x)-$Laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent Sobolev space is presented‎. ‎Multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding Nehari manifold‎.