含Φ-Laplace算子和凹凸非线性项的拟线性椭圆型方程正解的分歧性

数学物理学报 ›› 2020, Vol. 40 ›› Issue (5): 1235-1247.

含Φ-Laplace算子和凹凸非线性项的拟线性椭圆型方程正解的分歧性

王明旻(),贾高*()

^{上海理工大学理学院上海 200093}

收稿日期:2019-10-15 出版日期:2020-10-26 发布日期:2020-11-04
通讯作者: 贾高 E-mail:745136863@qq.com;gaojia89@163.com
作者简介:王明旻, E-mail:745136863@qq.com
基金资助:
国家自然科学基金(11171220)

Bifurcation of Positive Solutions for Quasilinear Elliptic Equations with Φ-Laplacian Operator and Concave-Convex Nonlinearities

Mingmin Wang(),Gao Jia*()

^{School of Science, University of Shanghai for Science and Technology, Shanghai 200093}

Received:2019-10-15 Online:2020-10-26 Published:2020-11-04
Contact: Gao Jia E-mail:745136863@qq.com;gaojia89@163.com
Supported by:
the NSFC(11171220)

摘要/Abstract

摘要：

该文利用临界点理论、截断技巧和比较原理，研究了一类含Φ-Laplace算子和凹凸非线性项的拟线性椭圆型方程正解关于参数$\lambda$的分歧性，进一步得到了最小正解的存在性和关于参数$\lambda$的单调性.

关键词: 拟线性椭圆型方程, 分歧性, 截断技巧

Abstract:

In this paper, we study the bifurcation of positive solutions about parameter $\lambda$ for the quasilinear elliptic equations with Φ-Laplacian operator and concave-convex nonlinearities by using the critical point theory, appropriate truncation and comparison techniques. Furthermore, we obtain the existence of the smallest positive solution and the monotonicity with respect to parameter $\lambda$.

Key words: Quasilinear elliptic equation, Bifurcation, Truncation techniques

中图分类号:

O175.3

王明旻,贾高. 含Φ-Laplace算子和凹凸非线性项的拟线性椭圆型方程正解的分歧性[J]. 数学物理学报, 2020, 40(5): 1235-1247.

Mingmin Wang,Gao Jia. Bifurcation of Positive Solutions for Quasilinear Elliptic Equations with Φ-Laplacian Operator and Concave-Convex Nonlinearities[J]. Acta mathematica scientia,Series A, 2020, 40(5): 1235-1247.

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