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Existence of two solutions for quasilinear periodic differential equations with discontinuities

Nikolaos S. Papageorgiou, Francesca Papalini (2002)

Archivum Mathematicum

In this paper we examine a quasilinear periodic problem driven by the one- dimensional p -Laplacian and with discontinuous forcing term f . By filling in the gaps at the discontinuity points of f we pass to a multivalued periodic problem. For this second order nonlinear periodic differential inclusion, using variational arguments, techniques from the theory of nonlinear operators of monotone type and the method of upper and lower solutions, we prove the existence of at least two non trivial solutions,...

Existence Principles for Singular Vector Nonlocal Boundary Value Problems with φ -Laplacian and their Applications

Staněk, Svatoslav (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Existence principles for solutions of singular differential systems ( φ ( u ' ) ) ' = f ( t , u , u ' ) satisfying nonlocal boundary conditions are stated. Here φ is a homeomorphism N onto N and the Carathéodory function f may have singularities in its space variables. Applications of the existence principles are given.

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