PERIODIC SOLUTIONS FOR INDEFINITE SINGULAR EQUATIONS WITH SINGULARITIES IN THE SPATIAL VARIABLE AND NON-MONOTONE NONLINEARITY

被引：2

作者：

Amster, Pablo ^{[1
]}

Zamora, Manuel ^{[2
]}

机构：

[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, Pabellon 1, RA-1428 Buenos Aires, DF, Argentina

[2] Univ Oviedo, GISDA, C Federico Garcia Lorca 18, Oviedo, Spain

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 10期

关键词：

Singular differential equations; indefinite singularity; periodic solutions; degree theory; Leray-Schauder continuation theorem; DIFFERENTIAL-EQUATIONS; 2-BODY PROBLEM; PHI-LAPLACIAN; SPHERE;

D O I：

10.3934/dcds.2018211

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

TWe prove the existence of T-periodic solutions for the second order non-linear equation (u'/root 1-u'(2))' = h(t)g(u), where the non-linear term g has two singularities and the weight function h changes sign. We find a relation between the degeneracy of the zeroes of the weight function and the order of one of the singularities of the non-linear term. The proof is based on the classical Leray-Schauder continuation theorem. Some applications to important mathematical models are presented.

引用

页码：4819 / 4835

页数：17

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