Existence of Positive Radial Solutions for Some Semilinear Elliptic Equations in Annulus

YAO Qing-liu; MA Qin-sheng

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YAO Qing-liu, MA Qin-sheng. Existence of Positive Radial Solutions for Some Semilinear Elliptic Equations in Annulus[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1296-1300.

Citation:

YAO Qing-liu, MA Qin-sheng. Existence of Positive Radial Solutions for Some Semilinear Elliptic Equations in Annulus[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1296-1300.

Citation:

YAO Qing-liu, MA Qin-sheng. Existence of Positive Radial Solutions for Some Semilinear Elliptic Equations in Annulus[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1296-1300.

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Existence of Positive Radial Solutions for Some Semilinear Elliptic Equations in Annulus

YAO Qing-liu¹,
MA Qin-sheng²

1.
Department of Applied Mathematics, Nanjing University of Economics, Nanjing 210003, P R China;
2.
College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, P R China

Received Date: 2000-04-21
Rev Recd Date: 2002-06-11
Publish Date: 2002-12-15

Abstract

Abstract

Applying Krasnoselc skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains,subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.
- second-order elliptic equation,
- annular domain,
- positve radial solution

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References(12)

References

[1]	NI Wei-ming,Nussbanm R D.Uniqueness and nonuniqueness for positive radial solutions of Δu+f(u,r)=0 [J].Comm Pure Appl Math,1985,38(1):67-108.
[2]	Bandle C,Coffman C V,Marcus M.Nonlinear elliptic problems in annular domains[J].J Differential Equations,1987,69(3):322-345.
[3]	LIN Song-sun.On the existence of positive radial solutions for nonlinear elliptic equations in annular domains[J].J Differential Equations,1989,81(2):221-233.
[4]	WANG Hai-yan.On the existence of positive solutions for semilinear elliptic equations in annulus[J].J Differential Equations,1994,109(1):1-7.
[5]	Erbe L H,HU Shou-chuan,WANG Hai-yan.Multiple positive solutions of some boundary value problems[J].J Math Anal Appl,1994,184(3):640-648.
[6]	Lions P L.On the existence of positive solutions of semilinear elliptic equations[J].SIAM Rev,1982,24(4):441-467.
[7]	姚庆六,白占兵.u⁽⁴⁾(t)-λh(t)f(u(t))=0的边值问题的正解存在性[J].数学年刊(A),1999,20(5):575-578.
[8]	姚庆六.方程Δu+g(\|X\|)f(u)=0的环上Dirichlet边值问题的正对径解的存在性[J].数学物理学报(A),2000,20(3):414-418.
[9]	姚庆六,王景荣.方程Δu+g(\|X\|)f(u)=0的环上Dirichlet边值问题的多重正对径解[J].系统科学与数学,2000,20(4):487-492.
[10]	姚庆六.广义Gelfand模型的正解[J].高校应用数学学报(A),2001,16(4):407-413.
[11]	姚庆六.一类奇异次线性两点边值问题的正解[J].应用数学学报,2001,24(4):522-526.
[12]	钟承奎,范先令,陈文源.非线性泛函分析引论[M].兰州:兰州大学出版社,1998,143-154.