Existence of positive solutions for multi-point resonance systems of differential equations with boundary value conditions

Abstract

It is difficult to study the existence of solutions for boundary value problems of differential equations at resonance, moreover, to get positive solutions of boundary value problems for differential equations at resonance is more difficult. To research this problem, the existence of positive solutions for a couple of different equations with multi-point boundary value conditions at resonance is studied. On the basis of previous researches, choosing a different operator, the equation is extended to a couple of different equations. By defining the correct norm in the product spaces which become Banach spaces, and using the Leggett-Williams norm-type theorem due to O'Regan and Zima, the nonlinear term satisfies reasonable assumptions, and the existence of positive solutions for a coupled of different equations with multi-point boundary value conditions at resonance is obtained.

Keywords

• other disciplines of ordinary differential equation
• boundary value problem
• resonance
• positive solution
• differential equation