Existence theory for functional p-Laplacian equations with variable exponents

• Published in: Nonlinear analysis Vol. 52; no. 2; pp. 557 - 572
• Main Authors: Cabada, Alberto, Pouso, Rodrigo L.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 2003; Elsevier
• Subjects: Boundary value problems; Exact sciences and technology; Functional equations; Mathematical analysis; Mathematics; Nonlinear equations; Ordinary differential equations; p-Laplacian; Sciences and techniques of general use; Upper and lower solutions; p-Laplacian; Upper and lower solutions; Nonlinear equations; Boundary value problems; Functional equations; Laplace operator; Existence theorem; Differential equation; Existence of solution; Theory; Functional equation; Laplace equation; Nagumo condition; Laplacian; Bounded solution; Non linear equation; Boundary value problem; Fixed point theorem; Equicontinuous function; Dirichlet problem; Lebesgue integral; Solvability
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/S0362-546X(02)00122-0

In this paper we consider the solvability of equations of the form − d dt ϕ(t,u,u(t),u′(t))=f(t,u,u(t),u′(t)) for a.e. t∈I=[a,b] subject to a general type of functional-boundary conditions which cover Dirichlet and periodic boundary data as particular cases. Our approach is that of upper and lower solutions together with growth restrictions of Nagumo's type. An example is provided where a p-Laplacian with variable p is shown to have a solution between given upper and lower solutions.