Variational Approach to Fourth-Order Impulsive Differential Equations with Two Control Parameters

被引：29
作者：
Afrouzi, Ghasem A. [1 ]
Hadjian, Armin [1 ]
Radulescu, Vicentiu D. [2 ,3 ]
机构：
[1] Univ Mazandaran, Fac Math Sci, Dept Math, Babol Sar, Iran
[2] Romanian Acad, Inst Math Simion Stoilow, Bucharest 014700, Romania
[3] Univ Craiova, Dept Math, Craiova 200585, Romania
来源：
RESULTS IN MATHEMATICS | 2014年 / 65卷 / 3-4期
关键词：
Impulsive differential equations; multiple solutions; variational methods; BOUNDARY-VALUE-PROBLEMS; MULTIPLE SOLUTIONS;
D O I：
10.1007/s00025-013-0351-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we are concerned with the multiplicity of solutions for a fourth-order impulsive differential equation with Dirichlet boundary conditions and two control parameters. Using variational methods and a three critical points theorem, we give some new criteria to guarantee that the impulsive problem has at least three classical solutions. We also provide an example in order to illustrate the main abstract results of this paper.
引用
收藏
页码：371 / 384
页数：14
相关论文
共 24 条
[1]  
Afrouzi GA, 2012, B MATH SOC SCI MATH, V55, P343
[2]  
[Anonymous], 1995, World Sci. Ser. Nonlinear Sci., Ser. A., DOI DOI 10.1142/2892
[3]  
[Anonymous], 2010, Encyclopedia of Mathematics and its Applications
[4]  
Benchohra M., 2006, Impulsive Differential equations and Inclusions
[5]   Multiple symmetric solutions for a Neumann problem with lack of compactness [J].
Bisci, Giovanni Molica ;
Radulescu, Vicentiu .
COMPTES RENDUS MATHEMATIQUE, 2013, 351 (1-2) :37-42
[6]   Multiple solutions of generalized Yamabe equations on Riemannian manifolds and applications to Emden-Fowler problems [J].
Bonanno, Gabriele ;
Bisci, Giovanni Molica ;
Radulescu, Vicentiu .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (05) :2656-2665
[7]   Existence of three solutions for a non-homogeneous Neumann problem through Orlicz-Sobolev spaces [J].
Bonanno, Gabriele ;
Bisci, Giovanni Molica ;
Radulescu, Vicentiu .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (14) :4785-4795
[8]   Three weak solutions for elliptic Dirichlet problems [J].
Bonanno, Gabriele ;
Bisci, Giovanni Molica .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 382 (01) :1-8
[9]   Existence of three solutions for a perturbed two-point boundary value problem [J].
Bonanno, Gabriele ;
Chinni, Antonia .
APPLIED MATHEMATICS LETTERS, 2010, 23 (07) :807-811
[10]   On the structure of the critical set of non-differentiable functions with a weak compactness condition [J].
Bonanno, Gabriele ;
Marano, Salvatore A. .
APPLICABLE ANALYSIS, 2010, 89 (01) :1-10
123