Two point boundary value problems for ordinary differential systems with generalized variable exponents operators

Abstract

In recent years an increasing interest in more general operators generated by Musielak-Orlicz functions is under development since they provided, in principle, a unified treatment deal with ordinary and partial differential equations with operators containing the p-Laplace operator, the phi-Laplace operator, operators with variable exponents and the double phase operators. These kind of consideration lead us in Garcia-Huidobro et al. (2024), to consider problems containing the operator (S(t, u ')) where ' = d/dt and look for period solutions systems of nonlinear systems of differential equations. In this paper we extend our approach to deal with systems of differential equations containing the operator (S(t, u ')) this time under Dirichlet, mixed and Neumann boundary conditions. As in Garcia-Huidobro et al. (2024) our approach is to work in C-1 spaces to obtain suitable abstract fixed points theorems from which several applications are obtained, including problems of Lienard and Hartman type.