Homoclinic solutions for ordinary p-Laplacian systems with a coercive potential

被引：64

作者：

Tang, X. H. ^{[1
]}

Xiao, Li ^{[1
]}

机构：

[1] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410083, Hunan, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 3-4期

关键词：

Homoclinic solutions; p-Laplacian systems; Coercive potential; PERIODIC-SOLUTIONS; 2ND-ORDER SYSTEMS; ORBITS; EXISTENCE;

D O I：

10.1016/j.na.2008.11.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A result for the existence of homoclinic orbits is obtained for p-Laplacian systems d/dt (vertical bar(u) over dot(t)vertical bar(p-2)(u) over dot(t)) = del F(t, u(t)) + f(t), where p > 1, u is an element of R-n, F is an element of C-1(R x R-n, R) is T-periodic with respect to t and f : R -> R-n is a continuous and bounded function such that F(t, x ) >= F(t, 0) + b vertical bar x vertical bar(mu) and integral(R) vertical bar f(t)vertical bar(mu/(mu-1)) dt < infinity for some b > 0 and mu > 1. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：1124 / 1132

页数：9

共 23 条

[1]

Ambrosetti A., 1993, REND SEMIN MAT U PAD, V89, P177, DOI DOI 10.1016/0165-0114(92)90069-G

[2]

[Anonymous], 2005, APPL MATH, DOI DOI 10.1007/S10492-005-0037-8

[3] Existence of homoclinic solutions for a class of time-dependent Hamiltonian systems [J].

Carriao, PC ;

Miyagaki, OH .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 230 (01) :157-172

[4]

Coti-Zelati V, 1991, J AM MATH SOC, V4, P693

[5] HOMOCLINIC ORBITS FOR FIRST-ORDER HAMILTONIAN-SYSTEMS [J].

DING, YH ;

LI, SJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 189 (02) :585-601

[6] Homoclinic solutions for a class of the second order Hamiltonian systems [J].

Izydorek, M ;

Janczewska, J .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 219 (02) :375-389

[7] Homoclinic solutions for nonautonomous second order Hamiltonian systems with a coercive potential [J].

Izydorek, Marek ;

Janczewska, Joanna .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 335 (02) :1119-1127

[8] Ordinary p-Laplacian systems with nonlinear boundary conditions [J].

Jebelean, P ;

Morosanu, G .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 313 (02) :738-753

[9] Periodic solutions for nonlinear systems with p-Laplacian-like operators [J].

Manasevich, R ;

Mawhin, J .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 145 (02) :367-393

[10] Some boundary value problems for Hartman-type perturbations of the ordinary vector p-laplacian [J].

Mawhin, J .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2000, 40 (1-8) :497-503

← 1 2 3 →