Entire positive solutions for an inhomogeneous semilinear biharmonic equation

被引：4

作者：

Yang, Fen ^{[1
]}

机构：

[1] Wuhan Univ Sci & Technol, Coll Sci, Dept Informat & Computat, Wuhan 430081, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 70卷 / 03期

关键词：

Inhomogeneous biharmonic equation; Entire positive solution; Decay rate; ELLIPTIC EQUATION; EXISTENCE;

D O I：

10.1016/j.na.2008.02.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the entire positive Solutions for the inhomogeneous biharmonic equation - Delta(2)u + u(p) + f(x) = 0 in R-n, (*) where Delta(2) is the biharmonic operator, p > 1, n >= 5 and 0 not equivalent to f is an element of C(R-n) is a given nonnegative function, Based on the results on the biharmonic equation in [Q.Y. Dai, Entire positive solutions for inhomogeneous semilinear elliptic systems, Glasgow Math. J 47 (2005) 97-114], we obtain the optimal "decay coefficient" of the inhomogeneous term f for existence and nonexistence. And also, we obtain that there exist at least two types of decay solutions at infinity with the assumptions on f. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：1365 / 1376

页数：12

共 50 条

[11] Entire Solutions for an Inhomogeneous Bistable Discrete Diffusive Equation [J].

Yang, Xing-Xing ;

Zhang, Guo-Bao .

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2023, 46 (02)

[12] EXISTENCE OF ENTIRE POSITIVE SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC SYSTEMS [J].

Zhang, Zhijun .

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2010,

[13] A note on the positive solutions of an inhomogeneous elliptic equation on Rn [J].

Deng, Yinbin ;

Li, Yi ;

Yang, Fen .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (02) :670-680

[14] Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation [J].

Guo, Zongming ;

Wei, Juncheng ;

Zhou, Feng .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (02) :1188-1224

[15] Asymptotic behavior of positive solutions of inhomogeneous semilinear elliptic equations [J].

Bae, S .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 51 (08) :1373-1403

[16] Entire nodal solutions of a semilinear elliptic equation and their effect on concentration phenomena [J].

Clapp, Monica ;

Srikanth, P. N. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 437 (01) :485-497

[17] Entire solutions with moving singularities for a semilinear heat equation with a critical exponent [J].

Takahashi, Jin .

PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2022, 3 (02)

[18] Existence of entire positive solutions for semilinear elliptic systems with gradient term [J].

Jiang, Xiaowei ;

Lv, Xuezhe .

ARCHIV DER MATHEMATIK, 2012, 99 (02) :169-178

[19] Existence of entire positive solutions for semilinear elliptic systems with gradient term [J].

Xiaowei Jiang ;

Xuezhe Lv .

Archiv der Mathematik, 2012, 99 :169-178

[20] A remark on the existence of entire positive solutions for a class of semilinear elliptic systems [J].

Li, Hong ;

Zhang, Pei ;

Zhang, Zhijun .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 365 (01) :338-341

← 1 2 3 4 5 →