Natural Runge-Kutta and Projection Methods.
In the present paper we give general nonuniqueness results which cover most of the known nonuniqueness criteria. In particular, we obtain a generalization of the nonuniqueness theorem of Chr. Nowak, of Samimi’s nonuniqueness theorem and of Stettner’s nonuniqueness criterion.
The paper is devoted to the study of the properties of the Fučík spectrum. In the first part, we analyse the Fučík spectra of the problems with one second order ordinary differential equation with Dirichlet, Neumann and mixed boundary conditions and we present the explicit form of nontrivial solutions. Then, we discuss the problem with two second order differential equations with mixed boundary conditions. We show the relation between the Dirichlet boundary value problem and mixed boundary value...