一类奇异的半线性双调和方程的正整解

Acta mathematica scientia,Series A ›› 2003, Vol. 23 ›› Issue (6): 729-734.

• Articles • Previous Articles Next Articles

The |Positive |Entire |Solutions |of a |Class |of Singular |Semilinear |Biharmonic |Equations

XIE Chang-Qing

漳州师范学院数学系漳州 363000

Online:2003-12-25 Published:2003-12-25
Supported by:
福建省教育厅资助项目(JA02247)

Abstract

Abstract:

In the paper, the author's aims are to establish the theorems of existence of po sitive radial symmetric entire solutions for a class of singular semilinear biha rmonic equations, to present the properties of the solutions, and to extend the result of paper ［7］.

Key words: Biharmonic equation, Positive entire solution; , Relative , com pactness, Fixed , point , theomrem； Continuous mapping.

CLC Number:

35J

[1]	Xiaojin Bai,Jianfeng Zhu. Boundary Schwarz Lemma for Solutions to a Class of Inhomogeneous Biharmonic Equations [J]. Acta mathematica scientia,Series A, 2022, 42(6): 1633-1639.
[2]	Gui Bao,Qian Sun. Existence and Multiplicity of Sign-Changing Solutions for a Bi-Harmonic Equation with Sublinear Nonlinearity [J]. Acta mathematica scientia,Series A, 2020, 40(5): 1186-1191.
[3]	Xiaohang Ou. Sufficient and Necessary Condition for the Existence of Positive Entire Solutions of a Nonlinear Biharmonic Equations on ${{\mathbb{R}}^{N}}$ [J]. Acta mathematica scientia,Series A, 2019, 39(3): 535-544.
[4]	Yang Fen. Decay Rate of Solutions to An Inhomogenerous Semilinear Biharmonic Equation in Entire Space [J]. Acta mathematica scientia,Series A, 2015, 35(2): 282-287.
[5]	ZHANG Ya-Jing. Multiple Solutions for Biharmonic Equations with Concave-Convex Nonlinearities [J]. Acta mathematica scientia,Series A, 2013, 33(2): 353-365.
[6]	SHU Lan-Ping, LI Gang. Fixed Point \|Theorems for Asymptotically Nonexpansive Type Semigroups in General Banach Spaces [J]. Acta mathematica scientia,Series A, 2009, 29(2): 290-296.
[7]	Xu Xingye. The Positive Entire Solutions for a Class of Nonlinear Biharmonic Equations with Singularity on Rⁿ [J]. Acta mathematica scientia,Series A, 2009, 29(1): 87-93.
[8]	Tang Chunxia; Zhang Zhengjie. The Existence of a Nontrivial Solution for Biharmonic Equation [J]. Acta mathematica scientia,Series A, 2008, 28(2): 256-265.
[9]	XIONG Hui, CHEN Yao-Tian. On the Dirichlet Problem of Semilinear Singular critical Biharmonic Equations [J]. Acta mathematica scientia,Series A, 2005, 25(3): 299-306.
[10]	MO A-Yang, LIN Xiao-Ning, JIANG Da-Qing. A New Existence Theory for Positive Periodic Solutions to Volterra Integro differential Equations [J]. Acta mathematica scientia,Series A, 2005, 25(3): 367-373.
[11]	SHEN Jian-Zhong, YI Fa-Huai. A Reaction Diffusion's Free Boundary Problem [J]. Acta mathematica scientia,Series A, 2003, 23(2): 183-192.
[12]	KANG Dong-Sheng, DENG Yin-Bin. SobolevHardy Inequalities and Some Critical Biharmonic Problems [J]. Acta mathematica scientia,Series A, 2003, 23(1): 106-114.
[13]	Zeng Xianzhong Deng Yinbin. Existence of Multiple Solutions for a Semilinear Biharmonic-Equation with Critical Exponent [J]. Acta mathematica scientia,Series A, 2000, 20(4): 547-554.
[14]	Guo Zhenhua, Deng Yinbin. Existence of muliple positive solution for Δ^2 α=λμ+μ^(N+4)/(N-4)+μf(x) [J]. Acta mathematica scientia,Series A, 1999, 19(2): 138-148.
[15]	Xu Xingye. The Positive Entire Solutions of Class of Singular Nonlinear Biharmonic Equations [J]. Acta mathematica scientia,Series A, 1998, 18(S1): 167-173.

The |Positive |Entire |Solutions |of a |Class |of Singular |Semilinear |Biharmonic |Equations

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10