EXISTENCE OF n POSITIVE SOLUTIONS TO SECOND-ORDER MULTI-POINT BOUNDARY VALUE PROBLEM AT RESONANCE

Abstract

Abstract. The existence of n positive solutions is established for secondorder multi-point boundary value problem at resonance where n is an arbitrary natural number. The proof is based on a theory of fixed point index for A-proper semilinear operators defined on cones due to Cremins.

On the Existence of Positive Solutions of Resonant and Nonresonant Multipoint Boundary Value Problems for Third-Order Nonlinear Differential Equations

“…It is well known that the problem of existence of positive solution for nonlinear BVP is very difficult when the resonant case is considered. Only few works gave the approach in this area for first-and second-order differential equations [27][28][29][30][31][32][33][34]. To our best knowledge, few paper dealt with the existence result of positive solution for resonant third-order boundary value problems.…”