Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem

By Pedro J. Torres. 2003

332 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2a091e3ae0a063f386a81449191aeafce4914292

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In Applied Mathematics

In Geometry and Topology

In Numerical Analysis

Citations in the corpus

Positive periodic solutions of singular systems with a parameter (2010, background): “For a non-constant function ai(t), there is a criterion discussed in [25,31] to guarantee the positiveness of the Green’s functions.”
Periodic solutions of singular systems without the strong force condition (2007, background): “As a final comment, let us emphasize that our standing hypothesis (A) (nonnegativeness) is weaker than the required condition in [15, 7, 9] (positiveness of the Green’s function) and allows, for instance, the critical case a(t) ≡ π T .”
Solvability of Nonlinear Singular Problems for Ordinary Differential Equations (2009, result): “Further results were delivered later also by Bonheure and De Coster [45] and Torres [192].”
Periodic solutions of second order non-autonomous singular dynamical systems (2007, background): “For a non-constant function a(t), there is an L-criterion proved in [26], which is given in the following lemma for the sake of completeness.”
Multiplicity of positive periodic solutions to superlinear repulsive singular equations (2005, unknown): “Recently, Rachunková et al.[18] and Torres[20] have obtained the existence results in the presence of weak singularities.”
Chapter 7 Singularities and Laplacians in Boundary Value Problems for Nonlinear Ordinary Differential Equations (2006, background): “Simultaneously, Torres [152] noticed that having a thorough analysis of the sign properties of the related Green’s functions, solvability of the periodic problem with a weak singularity can be ensured also by the Krasnoselskii fixed point theorem.”
Applications of Schauder's fixed point theorem to singular differential equations (2007, methodology): “For a non-constant function a(t), there is an L−criterion proved in [15].”
Periodic orbits of radially symmetric Keplerian-like systems: A topological degree approach (2008, unknown): “See also, among others, [16,17,22,30].”
Weak singularities may help periodic solutions to exist (2007, background): “As a corollary, we obtain an alternative criterion to those obtained in [16,21] for Eq.”
Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem (2008, background): “[5], Li [7], O’Regan and Wang [10], Torres [11], and Zhang and Wang [13].”
Periodic solutions for second order singular damped differential equations (2012, methodology): “Some classical tools have been used to study singular differential equations in the literature, including the method of upper and lower solutions [2, 25], degree theory [30, 31, 33], some fixed point theorems in cones for completely continuous operators [11, 26, 27], Schauder’s fixed point theorem [”