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Existence of periodic solutions for quasilinear ordinary differential eqasilinear ordinary diefferential equations with discontinuities

Matzakos N., Papageorgiou N.

Demonstratio Mathematica

2000

Vol. 33, nr 4

753-770

We consider a quasilinear differential equation with discontinuous right hand side and periodic boundary conditions. To obtain an existence theory we pass to a relevant multivalued variant of the original problem, which we solve. Our approach is a mixture of the variational method (for nonsmooth locally Lipschitz functionals) and of the method of upper and Iower solutions. The mixing of these two techniques is made possible by a nonresonance condition below the first nonzero eigenvalue of the one-dimensional p-Laplacian with periodic boundary conditions.