SIGN-CHANGING SOLUTIONS TO A CLASS OF NONLINEAR EQUATIONS INVOLVING THE p-LAPLACIAN

被引：3

作者：

Wang, Wei-Chuan ^{[1
,2
]}

Cheng, Yan-Hsiou ^{[3
]}

机构：

[1] Natl Quemoy Univ, Dept Civil Engn & Engn Management, Kinmen 892, Taiwan

[2] Ctr Gen Educ, Kinmen 892, Taiwan

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

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2017年 / 47卷 / 03期

关键词：

Sign-changing; radial solution; nonlinear p-Laplacian equation; MULTIPLE POSITIVE SOLUTIONS; BOUNDARY-VALUE-PROBLEMS; RADIAL SOLUTIONS; EIGENVALUES; EXISTENCE; BIFURCATION;

D O I：

10.1216/RMJ-2017-47-3-971

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with a class of nonlinear problems -(r(n-1) vertical bar u'vertical bar(p-2)u')'+r(n-1) q(r)vertical bar u vertical bar(P-2)u = r(n-1)w(r)f(u) in (0, 1), where 1 <= n < p < infinity and = d/dr. We study the existence of nodal solutions to this nonautonomous system. We give necessary and sufficient conditions for the existence of sign-changing solutions and also observe an application related to the case of multi-point boundary conditions. Methods used here are energy function control, shooting arguments and Priifer-type substitutions.

引用

页码：971 / 996

页数：26

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