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A nonlinear periodic system with nonsmooth potential of indefinite sign

Michael E. Filippakis, Nikolaos S. Papageorgiou (2006)

Archivum Mathematicum

In this paper we consider a nonlinear periodic system driven by the vector ordinary p -Laplacian and having a nonsmooth locally Lipschitz potential, which is positively homogeneous. Using a variational approach which exploits the homogeneity of the potential, we establish the existence of a nonconstant solution.

A note on rapid convergence of approximate solutions for second order periodic boundary value problems

Rahmat A. Khan, Bashir Ahmad (2005)

Archivum Mathematicum

In this paper, we develop a generalized quasilinearization technique for a nonlinear second order periodic boundary value problem and obtain a sequence of approximate solutions converging uniformly and quadratically to a solution of the problem. Then we improve the convergence of the sequence of approximate solutions by establishing the convergence of order k ( ...

A note on solutions of semilinear equations at resonance in a cone

Bogdan Przeradzki (1993)

Annales Polonici Mathematici

A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).

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