EXISTENCE OF SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR p-LAPLACIAN BOUNDARY VALUE PROBLEM

被引：1

作者：

Lian, Wei-Cheng ^{[1
]}

Wang, Wei-Chuan ^{[2
]}

Cheng, Yan-Hsiou ^{[3
]}

机构：

[1] Natl Kaohsiung Marine Univ, Dept Informat Management, Kaohsiung 811, Taiwan

[2] Natl Quemoy Univ, Ctr Gen Educ, Kinmen 892, Taiwan

[3] Natl Taipei Univ Educ, Dept Math & Informat Educ, Taipei 106, Taiwan

来源：

ANALYSIS AND APPLICATIONS | 2013年 / 11卷 / 02期

关键词：

Existence; sign-changing solutions; nonlinear p-Laplacian; boundary value problem; POSITIVE SOLUTIONS; EQUATIONS;

D O I：

10.1142/S0219530513500048

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the nonlinear one-dimensional p-Laplacian equation -(y'((p-1)))' + (p - 1)q(x)y((p-1)) = (p - 1)w(x)f(y) on (0,1), where p > 1, y((p-1)) = vertical bar y vertical bar(p-1)sgn y = vertical bar y vertical bar(p-2)y, with linear separated boundary conditions. We give sufficient conditions for the existence of solutions with prescribed nodal properties concerning the behavior of f(s)/s((p-1)) when s is at infinity and zero, respectively. These results are more general and complementary than previous known ones for the case when p = 2 and q is nonnegative.

引用

页数：15

共 50 条

[1] SIGN-CHANGING SOLUTIONS FOR THE BOUNDARY VALUE PROBLEM INVOLVING THE FRACTIONAL p-LAPLACIAN
Wu, Pengcheng
Zhou, Yuying
[J]. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2021, 57 (02) : 597 - 619
[2] Existence of sign-changing solutions to a Dirichlet problem with p-Laplacian and weights
Lin, Lishan
Li, Yongqing
[J]. ADVANCED NONLINEAR STUDIES, 2007, 7 (02) : 211 - 235
[3] POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR p-LAPLACIAN WITH SIGN-CHANGING NONLINEAR TERMS
Li, Xiangfeng
Xu, Wanyin
[J]. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2010, 47 (02) : 411 - 422
[4] A new existence result for the boundary value problem of p-Laplacian equations with sign-changing weights
Xianghui Xu
[J]. Proceedings - Mathematical Sciences, 2019, 129
[5] On the existence of sign-changing radial solutions to nonlinear p-Laplacian equations in Rn
Wang, Wei-Chuan
Cheng, Yan-Hsiou
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 102 : 14 - 22
[6] The existence of positive solutions for nonlinear boundary system with p-Laplacian operator based on sign-changing nonlinearities
Xu, Fuyi
[J]. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2010, (79) : 1 - 14
[7] Existence of solutions for a nonlinear fractional p-Laplacian boundary value problem
I. Merzoug
A. Guezane-Lakoud
R. Khaldi
[J]. Rendiconti del Circolo Matematico di Palermo Series 2, 2020, 69 : 1099 - 1106
[8] CONSTANT-SIGN AND SIGN-CHANGING SOLUTIONS OF A NONLINEAR EIGENVALUE PROBLEM INVOLVING THE p-LAPLACIAN
Carl, Siegfried
Motreanu, Dumitru
[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2007, 20 (03) : 309 - 324
[9] Existence of solutions for a nonlinear fractional p-Laplacian boundary value problem
Merzoug, I.
Guezane-Lakoud, A.
Khaldi, R.
[J]. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2020, 69 (03) : 1099 - 1106
[10] On sign-changing and multiple solutions of the p-Laplacian
Zhang, ZT
Li, SJ
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 197 (02) : 447 - 468

← 1 2 3 4 5 →