Extremal solutions of strongly nonlinear discontinuous second-order equations with nonlinear functional boundary conditions
The authors study a \(\phi\)-Laplacian problem with nonlinear functional boundary conditions and discontinuous right-hand side \(f\). Assuming that \(f\) satisfies an appropriate Nagumo condition, they prove the existence of at least one solution to this problem using the method of upper and lower solutions. Moreover, they prove the existence of extremal solutions and apply the monotone iterative technique by assuming certain additional hypotheses. The results obtained widely improve those from a previous paper by the same authors [Nonlinear Anal., Theory Methods Appl. 35A, No. 2, 221-231 (1999; Zbl 0920.34029)].
discontinuous ordinary differential equations
scientific article; zbMATH DE number 1532914
scientific article