A. Cabada and J. Tomeček

Existence of Extremal Solutions for Nonlinear Discontinuous Impulsive Functional $\Phi$-Laplacian Equations with Nonlinear Discontinuous Functional Boundary Conditions

abstract:
We derive sufficient conditions for the existence of extremal solutions for a second order nonlinear functional $\phi$-Laplacian boundary value problems with impulses, subject to boundary value conditions of general type which cover Dirichlet and multipoint boundary data as particular cases. Our approach is that of upper and lower solutions together with growth restrictions of Nagumo's type. Discontinuous functional dependence of the nonlinear data and the boundary conditions are allowed.

Mathematics Subject Classification: 34B37 (Primary), 34B15, 34B27 (Secondary)

Key words and phrases: Boundary value problem; impulses; lower and upper solutions; functional dependence; $\phi$-Laplacian; extremal solutions