NONNEGATIVE OSCILLATIONS FOR A CLASS OF DIFFERENTIAL EQUATIONS WITHOUT UNIQUENESS: A VARIATIONAL APPROACH

被引：5

作者：

Angel Cid, Jose ^{[1
]}

Sanchez, Luis ^{[2
]}

机构：

[1] Univ Vigo, Dept Matemat, Campus Ourense, Orense 32004, Spain

[2] Univ Lisbon, Fac Ciencias, CMAFcIO, P-1749016 Lisbon, Portugal

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2020年 / 25卷 / 02期

关键词：

Periodic solution; regular equation; critical point theory; mountain pass theorem; Liebau phenomenon; MODELS;

D O I：

10.3934/dcdsb.2019253

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We deal with the existence of nonnegative and nontrivial T-periodic solutions for the equation x '' = r (t)x(alpha) - s(t)x(beta) where r and s are continuous T-periodic functions and 0 < alpha < beta < 1. This equation has been studied in connection with the valveless pumping phenomenon and we will take advantage of its variational structure in order to guarantee its solvability by means of the mountain pass theorem of Ambrosetti and Rabinowitz.

引用

页码：545 / 554

页数：10

共 16 条

[1] On the pumping effect in a pipe/tank flow configuration with friction [J].

Angel Cid, Jose ;

Propst, Georg ;

Tvrdy, Milan .

PHYSICA D-NONLINEAR PHENOMENA, 2014, 273 :28-33

[2]

[Anonymous], BIRKHAUSER ADV TEXTS, DOI DOI 10.1007/978-3

[3] THE MONOTONICITY OF THE PERIOD FUNCTION FOR PLANAR HAMILTONIAN VECTOR-FIELDS [J].

CHICONE, C .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1987, 69 (03) :310-321

[4]

Chouikha A. R., 2005, APPL MATH, V32, P305

[5]

Chow S.-N., 1986, CAS PEST MAT FYS, V111, P14, DOI DOI 10.21136/CPM.1986.118260

[6]

Chow S-N., 1986, asopis Pst. Mat, V111, P89

[7] New results for the Liebau phenomenon via fixed point index [J].

Cid, J. A. ;

Infante, G. ;

Tvrdy, M. ;

Zima, M. .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2017, 35 :457-469

[8] A topological approach to periodic oscillations related to the Liebau phenomenon [J].

Cid, J. A. ;

Infante, G. ;

Tvrdy, M. ;

Zima, M. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 423 (02) :1546-1556

[9] Travelling wave profiles in some models with nonlinear diffusion [J].

Coelho, Isabel ;

Sanchez, Luis .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 235 :469-481

[10]

Gavioli A, 2016, DIFFER INTEGRAL EQU, V29, P665

← 1 2 →