A topological degree approach to a nonlocal Neumann problem for a system at resonance

Abstract

In this paper, we investigate the existence of solutions for a system of second-order differential equations with two nonlocal Neumann boundary conditions at resonance. The existence results are obtained by applying the Mawhin continuation theorem, where the required a priori estimates are derived using some conditions of the Nirenberg type.Mathematics Subject Classification. Primary 34B10; Secondary 34B15, 47H10, 54H25.where γ(t) = t and δ(t) = 1. This means that if (1.4) holds, then the homogeneous linear problem corresponding to (1.1), that is,has nontrivial solutions. In particular, (1.4) is satisfied if(1.5)(1.6)Vol. 21 (2019) Nonlocal Neumann problem at resonance

Positive solutions of nonlocal fractional boundary value problem involving Riemann-Stieltjes integral condition

“…Recently, some interesting results about the existence of positive solutions for nonlinear fractional differential equations involving the Riemann-Stieltjes integral boundary condition have been reported [2,10,13,14,15,16,17,18,19,20,21,22,3,23,24,25].…”