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Three Solutions Theorem for a Quasilinear Dirichlet Boundary Value Problem

Goncerz P.

Schedae Informaticae

2012

Vol. 21

159--168

We consider a Dirichlet boundary value problem driven by the p-Laplacian with the right hand side being a Carathéodory function. The existence of solutions is obtained by the use of a special form of the three critical points theorem.

Some remarks on Carathéodory conditions

Shragin I.V.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2005

Vol. 45, [Z] 1

131--135

Let [formula] be metric spaces. For the maps from [formula] the notionsof supmeasurability, standardness and Carathéodory conditions are considered, and the logical relations between these notions are discussed.

On the solution set of a vector Duffing equation

Papalini F., Papageorgiu N. S.

Demonstratio Mathematica

2002

Vol. 35, nr 4

763-772

In this paper we consider a vector Duffing equation with periodic boundary conditions. First we prove an existence result assuming on f(t,x) Caratheodory type conditions. Then by imposing also a monotonicity assumption we show that the solution set is acyclic.

Approximate Caratheodory selections

Kucia A., Nowak A.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 1

81-87

We give general theorems on the existence of single-valued Caratheodory approximations of an upper Caratheodory multifunction. Then we apply these results to multifunctions with convex, decomposable or satisfying the UV[sup omega]-property values.