Multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces

By Daqing Jiang, Jifeng Chu, Donal O'Regan, Ravi P. Agarwal. 2003

70 citations recorded by the source corpus.

Abstract The existence of multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces is discussed in this paper. Our nonlinearity may be singular in its dependent variable and our analysis relies on a nonlinear alternative of Leray–Schauder type and on a fixed point theorem in cones.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3e666e5492ff58e3bb55a6554ae1abfb8996b828

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

Impulsive periodic solutions of first‐order singular differential equations (2008, background): “On the other hand, singular periodic problems without impulse effects have also been investigated extensively in the literature [4, 6, 12, 13, 17].”
Applications of Schauder's fixed point theorem to singular differential equations (2007, methodology): “These classical tools include the coincidence degree theory of Mawhin [11, 17, 19], the method of upper and lower solutions [1, 3] and some fixed point theorems in cones for completely continuous operators [8, 9, 15].”
Positive periodic solutions of singular systems with a parameter (2010, background): “on of the above systems is of interest because it is a non-collision periodic orbit of the singular systems. Periodic solutions of singular systems has been studied over many years, see, for example, [1,2,3,4,5,10,11,12,13,14,15,17] and [18,20,21,22,24,25,26,27,30]. One of the common assumptions to ”