PERIODIC SOLUTIONS FOR A BEAM EQUATION WITH CONCAVE-CONVEX NONLINEARITIES

被引：0

作者：

Liu, Jianhua ^{[1
]}

Ji, Shuguan ^{[1
]}

Feng, Zhaosheng ^{[2
]}

机构：

[1] Northeast Normal Univ, Ctr Math & Interdisciplinary Sci, Sch Math & Stat, Changchun 130024, Peoples R China

[2] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2024年

关键词：

Existence; multiplicity; periodic solution; beam equation; concave-convex nonlinearities; WAVE-EQUATION;

D O I：

10.3934/dcdss.2024198

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with the time-periodic solutions of the beam equation with concave-convex nonlinearities which describes the forced vibrations of the beam. In general, the sup er-linear term plays a dominated role at infinity and the sub-linear term plays a dominated role at 0. By setting a variational framework, we take advantage of the mini-max principle to obtain two sequences of time-periodic solutions with large energy and small energy, respectively.

引用

页数：14

共 25 条

[1] Existence of periodic solution for a class of beam equation via variational methods [J].

Alves, Claudianor O. ;

de Araujo, Bruno S. V. ;

Nobrega, Alannio B. .

MONATSHEFTE FUR MATHEMATIK, 2022, 197 (02) :227-256

[2] COMBINED EFFECTS OF CONCAVE AND CONVEX NONLINEARITIES IN SOME ELLIPTIC PROBLEMS [J].

AMBROSETTI, A ;

BREZIS, H ;

CERAMI, G .

JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 122 (02) :519-543

[3] Periodic solutions of a wave equation with concave and convex nonlinearities [J].

Bartsch, T ;

Ding, YH ;

Lee, C .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 153 (01) :121-141

[4] ON AN ELLIPTIC EQUATION WITH CONCAVE AND CONVEX NONLINEARITIES [J].

BARTSCH, T ;

WILLEM, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (11) :3555-3561

[5] Periodic solutions of superlinear beam and membrane equations with perturbations from symmetry [J].

Bartsch, T ;

Ding, YH .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 44 (06) :727-748

[6]

Chang K.C., 1986, Critical Point Theory and Applications

[7]

Chang K. C., 1982, MATH METHOD APPL SCI, V4, P194

[8] Existence of infinitely many periodic solutions for the radially symmetric wave equation with resonance [J].

Chen, Jianyi ;

Zhang, Zhitao .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (07) :6017-6037

[9] Infinitely many periodic solutions for a semilinear wave equation in a ball in Rn [J].

Chen, Jianyi ;

Zhang, Zhitao .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (04) :1718-1734

[10]

Choi Q-Heung, 2007, [Honam Mathematical Journal, 호남수학학술지], V29, P19

← 1 2 3 →