Positive solutions of multi-point boundary value problems at resonance

On a Singular Second-Order Multipoint Boundary Value Problem at Resonance

“…However to the best of our knowledge the corresponding problem for second-order differential equations at resonance and with a singularity had not received much attention in the literature. For recent results in these directions see [1,2,[4][5][6][7][8][9] and references therein.…”

Existence of nonnegative solutions for a fractional m-point boundary value problem at resonance

“…All authors read and approved the final manuscript. 1 Department of Mathematics, Hanshan Normal University, Chaozhou, Guangdong 521041, China.…”

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

“…Since then, great efforts have been devoted to the multi-point boundary value problems for more general nonlinear ordinary differential equations due to its theoretical challenge and its great potential applications; see for example [1,6,8,9,10,11,12,14,15,16,17,18,19,21,22,25,30,31,32,33,34,35,36,37,38,39] and the references therein. Some theorems and methods of nonlinear functional analysis have been applied to research on this problem, such as the method of topological degree and Leray-Schauder fixed point theorem [15,30,31,33,34,37], the upper and lower solutions method and monotone iterative technique [38], and Mawhin coincidence degree theory [21,22].…”

“…It is well known that the problem of existence of positive solutions to boundary value problem is very difficult when the resonant case is considered. To our best knowledge, only few papers deal with positive solutions to boundary value problems at resonance [1,12,14,16,25,32,35,36,39]. Recently, Yang and Shen [36] obtained the existence of a positive solution for problem (1.1) with resonant condition (…”