A monotone iterative scheme for a nonlinear second order equation based on a generalized anti–maximum principle

By Pedro J. Torres, Meirong Zhang. 2003

62 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/65f9e0e4da397bac190d2c7497712a723d924ad7

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Certain classes of potentials for p ‐Laplacian to be non‐degenerate (2005, background): “These ideas are used first in [18] and are very useful in many problems [2, 9, 11].”
Weak singularities may help periodic solutions to exist (2007, background): “For a nonconstant a(t), there is a L-criterion proved in [21] (the proof relies on an anti-maximum principle from [23]) which is given in the following lemma for the sake of completeness.”
On periodic solutions of second-order differential equations with attractive-repulsive singularities (2010, background): “The reference [14] provides sufficient conditions in the L-norm for φ(t) to verify property (P ).”
Multiplicity of positive periodic solutions to superlinear repulsive singular equations (2005, unknown): “In paper [20], Torres succeeded in overcoming this difficulty by using a newL-anti-maximum principle developed in [21] and obtained some new existence results to problem ( 1.”
Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem (2003, background): “Keywords: Periodic solution; Krasnoselskii fixed point theorem; Green’s function; Jumping nonlinearity; Singular equation”
Periodic solutions of singular systems without the strong force condition (2007, background): “For a non-constant a(t), there is no explicit expression of the Green’s function, but there is an L-criterion for the positiveness of the Green’s function proved in [15] (the proof relies on an anti-maximum principle from [16]) which is becoming standard in related literature (see for instance [7, 9”