Periodic solutions for nonlinear differential equations with maximal monotone terms

Abstract

We examine nonlinear periodic problems for scalar and vector differential equations involving a maximal monotone operator which is not necessarily defined everywhere. In the scalar case, the nonlinear differential operator depends on both x and x', linearly in x', while in the vector case the differential operator depends only on x' and is a generalization of the p-Laplacian. Our approach is based on the theory of operators of monotone type and on the Leray-Schauder principle.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1016/s0362-546x(02)00168-2

Keywords

periodic solutions, p-Laplacian, maximal monotone operators, pseudomonotone operator, yosida approximation, leray–schauder principle

Publication Date

2003

Journal Title

Nonlinear Analysis: Theory, Methods & Applications

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