Solvability Conditions Related to Nonlinear Monotone Potential Operators

Abstract

This paper deals with boundary value problems for the second order nonlinear differential equations with monotone potential operators of type Au := -del(k(|del u|(2))del u(x)) + q(u(2))u(x), x is an element of Omega subset of R-n. An analysis of nonlinear problems shows that the potential of the operator A as well as the potential of related boundary value problem play an important role not only for solvability of these problems and linearization of the nonlinear operator, but also for the strong convergence of solutions of corresponding linearized problems.