Variational approaches to impulsive elastic beam equations of Kirchhoff type

被引：22

作者：

Heidarkhani, Shapour ^{[1
]}

Afrouzi, Ghasem A. ^{[2
]}

Ferrara, Massimiliano ^{[3
]}

Moradi, Shahin ^{[2
]}

机构：

[1] Razi Univ, Dept Math, Fac Sci, Kermanshah 67149, Iran

[2] Univ Mazandaran, Dept Math, Fac Math Sci, Babol Sar, Iran

[3] Univ Mediterranea Reggio Calabria, Dept Law & Econ, Via Bianchi 2, I-89127 Reggio Di Calabria, Italy

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2016年 / 61卷 / 07期

关键词：

Multiple solutions; impulsive differential equation; fourth-order problem of Kirchhoff type; variational methods; critical point theory; BOUNDARY-VALUE PROBLEM; POSITIVE SOLUTIONS; DIFFERENTIAL-EQUATIONS; MULTIPLICITY; EXISTENCE; CONTROLLABILITY; SYSTEMS;

D O I：

10.1080/17476933.2015.1131681

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the existence of multiple solutions for impulsive fourth-order differential equations of Kirchhoff type. Using a variational method and some critical points theorems, we obtain some new criteria for guaranteeing that impulsive fourth-order differential equations of Kirchhoff type have three and infinitely many solutions. Some recent results are extended and improved. Some examples are presented to demonstrate the applications of our main results.

引用

页码：931 / 968

页数：38

共 64 条

[1] EXISTENCE OF THREE SOLUTIONS FOR A DOUBLY EIGENVALUE FOURTH-ORDER BOUNDARY VALUE PROBLEM [J].

Afrouzi, G. A. ;

Heidarkhani, S. ;

O'Regan, Donal .

TAIWANESE JOURNAL OF MATHEMATICS, 2011, 15 (01) :201-210

[2] Variational Approach to Fourth-Order Impulsive Differential Equations with Two Control Parameters [J].

Afrouzi, Ghasem A. ;

Hadjian, Armin ;

Radulescu, Vicentiu D. .

RESULTS IN MATHEMATICS, 2014, 65 (3-4) :371-384

[3] Positive solutions for a quasilinear elliptic equation of Kirchhoff type [J].

Alves, CO ;

Corrêa, FJSA ;

Ma, TF .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 49 (01) :85-93

[4]

[Anonymous], 1995, World Sci. Ser. Nonlinear Sci., Ser. A., DOI DOI 10.1142/2892

[5]

[Anonymous], ELECT J DIFFER EQU

[6]

[Anonymous], 1883, Mechanik

[7]

[Anonymous], 2005, ELECTRON J QUAL THEO

[8]

[Anonymous], 1989, Series in Modern Applied Mathematics

[9] On the well-posedness of the Kirchhoff string [J].

Arosio, A ;

Panizzi, S .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (01) :305-330

[10] Blow up at infinity of solutions of polyharmonic Kirchhoff systems [J].

Autuori, G. ;

Colasuonno, F. ;

Pucci, P. .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2012, 57 (2-4) :379-395

← 1 2 3 4 5 6 7 →