Abstract
By using the Banach contraction principle and the Leggett-Williams fixed point theorem, this paper investigates the uniqueness and existence of at least three positive solutions for a system of mixed higher-order nonlinear singular differential equations with integral boundary conditions: where the nonlinear terms , satisfy some growth conditions, are linear functionals given by , involving Stieltjes integrals with positive measures, and . We give an example to illustrate our result. MSC: 34B16, 34B18.
Highlights
The theory of boundary value problems with integral conditions for ordinary differential equations arises in different areas of applied mathematics and physics
To the best of our knowledge, there are many papers concerning the existence of positive solutions for nth order boundary value problems with different kinds of boundary conditions for system, results for the system ( . ) are rarely seen
By using fixed point index theory and a priori estimates achieved by utilizing some properties of concave functions, Xu and Yang [ ] showed the existence and multiplicity positive solutions for the system of the generalized Lidstone problems, where the system are mixed higher-order differential equations
Summary
1 Introduction The purpose of this paper is to establish the uniqueness and existence of at least three positive solutions for a system of mixed higher-order nonlinear singular differential equations with integral boundary conditions, The theory of boundary value problems with integral conditions for ordinary differential equations arises in different areas of applied mathematics and physics. To the best of our knowledge, there are many papers concerning the existence of positive solutions for nth order boundary value problems with different kinds of boundary conditions for system (see [ – ] and the references therein), results for the system
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