Asymptotic properties for solutions of differential equations with singular p(t)-Laplacian

被引：2

作者：

Dosla, Zuzana ^{[1
]}

Fujimoto, Kodai ^{[2
]}

机构：

[1] Masaryk Univ, Dept Math & Stat, Kotlarska 2, Brno 61137, Czech Republic

[2] Osaka Metropolitan Univ, Fac Liberal Arts Sci & Global Educ, Gakuen Cho 1-1,Naka Ku, Sakai, Osaka 5998531, Japan

来源：

MONATSHEFTE FUR MATHEMATIK | 2023年 / 201卷 / 01期

关键词：

Asymptotic behavior; Nonoscillatory solutions; Extremal solutions; Weakly increasing solutions; p(t)-Laplacian; Half-linear differential equations;

D O I：

10.1007/s00605-023-01835-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with the nonoscillatory solutions of the nonlinear differential equation (a(t)|x'|(p(t)-2)x')' +b(t)|x|(?-2)x = 0 involving "singular" p(t)-Laplacian. Sufficient conditions are given for the existence of extremal solutions, which do not exist in the conventional cases. In addition, we prove the coexistence of extremal solutions and weakly increasing solutions. Some examples are given to illustrate our results.

引用

页码：65 / 78

页数：14

共 50 条

[1] Asymptotic properties for solutions of differential equations with singular p(t)-Laplacian
Zuzana Došlá
Kōdai Fujimoto
Monatshefte für Mathematik, 2023, 201 : 65 - 78
[2] Singular solutions of nonlinear differential equations with p(t)-Laplacian
Bartusek, Miroslav
Fujimoto, Kodai
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (12) : 11646 - 11666
[3] Asymptotic behavior of solutions to differential equations with p(t)-Laplacian
Dosla, Zuzana
Fujimoto, Kodai
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2022, 24 (10)
[4] ASYMPTOTIC INTEGRATION OF DIFFERENTIAL EQUATIONS WITH SINGULAR p-LAPLACIAN
Medved, Milan
Pekarkova, Eva
ARCHIVUM MATHEMATICUM, 2016, 52 (01): : 13 - 19
[5] Homoclinic solutions of singular differential equations with φ-Laplacian
Rachunek, Lukas
Rachunkova, Irena
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2018, (72)
[6] Existence and asymptotic behavior of positive solutions to p(x)-Laplacian equations with singular nonlinearities
Zhang, Qihu
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2007, 2007 (1)
[7] Asymptotic solutions of differential equations with singular impulses
Aviltay, Nauryzbay
Akhmet, Marat
Zhamanshin, Akylbek
CARPATHIAN JOURNAL OF MATHEMATICS, 2024, 40 (03) : 581 - 598
[8] Singular solutions to p-Laplacian type equations
Kilpeläinen, T
ARKIV FOR MATEMATIK, 1999, 37 (02): : 275 - 289
[9] On the asymptotic behavior of solutions of differential equations with a singular nonlinearity
Astashova, I. V.
DIFFERENTIAL EQUATIONS, 2014, 50 (11) : 1551 - 1552
[10] On the asymptotic behavior of solutions of differential equations with a singular nonlinearity
I. V. Astashova
Differential Equations, 2014, 50 : 1551 - 1552

← 1 2 3 4 5 →