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

摘要

This paper is devoted to the study of the following implicit nonlinear discontinuous functional boundary value problem(IP)L0u(t)=f(t,u,L0u)fora.e.t∈I=[a,b],L1(u)=B1(u,L1(u)),0=L2(u(a),u(b)),whereL0u(t)=−ddtϕ(t,u(t),u′(t))−g(t,u,u(t),u′(t)),andL1(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.