On positive solutions for nonhomogeneous m-point boundary value problems with two parameters

Abstract

This paper is concerned with the existence, multiplicity, and nonexistence of positive solutions for nonhomogeneous m-point boundary value problems with two parameters. The proof is based on the fixed-point theorem, the upper-lower solutions method, and the fixed-point index. MSC: 34B10; 34B18

A survey on stationary problems, Green's functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions

“…Henderson and Luca in [74,75] presented some results for positive solutions of a system of nonlinear the second-order ODEs subject to multi-point BCs. Wang and An [224] investigated the existence, multiplicity, and nonexistence of positive solutions for nonhomogeneous m-point BVP with two parameters. Under conditions weaker than those used by Ma, Zhang and Ge [238] established various results on the existence and nonexistence of symmetric positive solutions to fourthorder BVP with integral BC.…”

Positive solutions for fractional differential equation involving the Riemann-Stieltjes integral conditions with two parameters

“…Due to the wide application of fractional order differential equations, there are many studies which focus on the solvability of fractional differential equations. For some recent results on this topic, see [1,4,6,7,9,11,12,14,15] and the references therein. El-Shahed [3] considered the following fractional order differential equation…”