Periodic solutions for nonlinear differential equations with maximal monotone terms
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.
periodic solutions, p-Laplacian, maximal monotone operators, pseudomonotone operator, yosida approximation, leray–schauder principle
Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Periodic solutions for nonlinear differential equations with maximal monotone terms." Nonlinear Analysis: Theory, Methods & Applications 52, no. 4 (2003): 1317-1330.
Nonlinear Analysis: Theory, Methods & Applications