Boundary value problems for nonlinear perturbations of vector p-Laplacian-like operators

Abstract

The aim of this paper is to obtain nonlinear operators in suitable function spaces whose fixed points coincide with the solutions of the nonlinear boundary value problems (φ(u)) = f(t, u, u), l(u, u) = 0, where l(u, u) = 0 denotes the Dirichlet, Neumann or periodic boundary conditions on [0, T ], φ : R → R is a suitable monotone homeomorphism and f : [0, T ]× R × R → R is a Carathéodory function. The special case where φ(u) is the vector p-Laplacian |u|u with p > 1, is considered, and the applications deal with asymptotically positive homogeneous nonlinearities and the Dirichlet problem for generalized Liénard systems. AMS 1991 Subject Classification : 34B15, 47 H 15, 47 H 05, 47 H 10, 47 H 11

Cite this paper

@inproceedings{Mansevich2011BoundaryVP, title={Boundary value problems for nonlinear perturbations of vector p-Laplacian-like operators}, author={Ra{\'u}l Man{\'a}sevich and J. Mawhin}, year={2011} }