Nontrivial solutions of boundary value problems for second-order functional differential equations

被引：10

作者：

Calamai, Alessandro ^{[1
]}

Infante, Gennaro ^{[2
]}

机构：

[1] Univ Politecn Marche, Dipartimento Ingn Ind & Sci Matemat, Via Brecce Bianche, I-60131 Ancona, Italy

[2] Univ Calabria, Dipartimento Matemat & Informat, I-87036 Cosenza, Italy

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2016年 / 195卷 / 03期

关键词：

Fixed point index; Affine cone; Nontrivial solution; Retarded functional differential equation; Nonlocal boundary condition; POSITIVE SOLUTIONS;

D O I：

10.1007/s10231-015-0487-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a theory for the existence of multiple nontrivial solutions for a class of perturbed Hammerstein integral equations. Our methodology, rather than to work directly in cones, is to utilize the theory of fixed point index on affine cones. This approach is fairly general and covers a class of nonlocal boundary value problems for functional differential equations. Some examples are given in order to illustrate our theoretical results.

引用

页码：741 / 756

页数：16

共 41 条

[31]

Nussbaum R.D., 2002, HDB DYNAMICAL SYSTEM, V2, P461, DOI DOI 10.1016/S1874-575X(02)80031-5

[32]

Nussbaum R. D., 1991, LECT NOTES MATH, V1537, P143

[33]

PICONE M, 1908, ANN SCUOLA NORM SUP, V10, P1

[34] A survey on stationary problems, Green's functions and spectrum of Sturm-Liouville problem with nonlocal boundary conditions [J].

Stikonas, Arturas .

NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2014, 19 (03) :301-334

[35] Positive periodic solutions of functional differential equations [J].

Wang, HY .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 202 (02) :354-366

[36] Positive solutions of nonlocal boundary value problems: A unified approach [J].

Webb, J. R. L. ;

Infante, Gennaro .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2006, 74 :673-693

[37] Existence of positive solutions for a thermostat model [J].

Webb, J. R. L. .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (02) :923-938

[38] Positive solutions of nonlocal boundary value problems involving integral conditions [J].

Webb, Jeff R. L. ;

Infante, Gennaro .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2008, 15 (1-2) :45-67

[39] Optimal constants in a nonlocal boundary value problem [J].

Webb, JRL .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (5-7) :672-685

[40]

WHYBURN WM, 1942, B AM MATH SOC, V48, P692

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