Implicit nonlinear discontinuous functional boundary value φ-Laplacian problems: extremality results

Authors:
Alberto Cabada;Seppo Heikkilä
Affiliations:
Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15706, Santiago de Compostela, Spain;Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014, Oulu, Finland
Venue:
Applied Mathematics and Computation
Year:
2002

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Abstract

This paper is devoted to the study of the following implicit nonlinear discontinuous functional boundary value problem (IP){L0u(t) = f(t,u,L0u) for a.e. t∈I = [a, b],, L1(u) =B1(u,L1(u)), 0=L2(u(a),u(b)), where L0u(t) = -d/dt φ(t,u(t),u'(t)) - g(t,u,u(t),u'(t)), and L1(u) = L1 (u(a),u(b),u'(a),u'(b),u).Supposing that there is a lower solution α and an upper solution β such that α ≤ β, the existence of extremal solutions lying between both functions is proved.