Generalization of Fredholm alternative for nonlinear differential operators
Non-Linear Analysis
Pairs of positive solutions for the one-dimensional p-Laplacian
Nonlinear Analysis: Theory, Methods & Applications
Topological degree and periodic solutions of differential inclusions
Nonlinear Analysis: Theory, Methods & Applications
Some boundary value problems for Hartman-type perturbations of the ordinary vector p-Laplacian
Nonlinear Analysis: Theory, Methods & Applications - Lakshmikantham's Legacy: A tribute on his 75th birthday
Ordinary Differential Equations
Ordinary Differential Equations
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In this paper we study nonlinear second-order differential inclusions involving the differential operator depending on both: unknown function x and its derivative x', a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and can be applied to the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain solutions for both the "convex" and "nonconvex' problems. Finally, we present the cases of special interest, which fit into our framework, illustrating the generality of our results.