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Some new generalizations of critical point theorems for locally Lipschitz functions

Chen J.

Journal of Applied Analysis

2008

Vol. 14, nr 2

193-208

In the present paper, some generalized critical points theorems for locally Lipschitz functions are given, and some classical important theorems are improved.

A sufficient condition for optimality in nondifferentiable invex programming

Antczak T.

Control and Cybernetics

2001

Vol. 30, no 4

431-437

In this paper sufficient optimality condition are established for a nonlinear programming problem without differentiability assumption on the data wherein Clarke's generalized gradient is used to define invexity.

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.