A Variational Inequality Theory with Applications to P $P$ -Laplacian Elliptic Inequalities

Abstract

The main purpose of this paper is to establish variational inequality theory in connection with demicontinuous $\psi_{p}$ -dissipative maps in reflexive smooth Banach spaces by considering the convergence of approximants. As an application of this variational inequality theory, existence, uniqueness and convergence of approximants of positive weak solution for $p$ -Laplacian elliptic inequalities are obtained under suitable conditions.