JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (4): 48-55.doi: 10.6040/j.issn.1671-9352.0.2016.485

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Existence of radial positive solutions of second-order semi-positone elliptic differential equations

LI Tao-tao   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2016-10-20 Online:2017-04-20 Published:2017-04-11

Abstract: We consider the existence of radial positive solutions of second-order semi-positone elliptic differential equationΔu+λg(|x|)f(u)=0, R1<|x|2,with Dirichlet and Robin boundary conditions, where g∈C([R1,R2],[0,+∞)), f∈C([0,+∞), R). The proof of the main results are based on the fixed point theorems in cones.

Key words: fixed point theorem, second-order elliptic differential equation, radial positive solutions, semipositone problem

CLC Number: 

  • O175.8
[1] EUNKYUNG K, RAMASWAMY M, SHIVAJI R. Uniqueness of positive radial solutions for a class of semipositone problems on the exterior of a ball[J]. Journal of Mathematical Analysis and Applications, 2015, 423(1):399-409.
[2] ADACHI S, WATANABE T. Uniqueness and non-degeneracy of positive radial solutions for quasilinear elliptic equations with exponential nonlinearity[J]. Nonlinear Analysis, 2014, 108(1):275-290.
[3] BANDLE C, KWONG M K. Semilinear elliptic problems in annular domains[J]. Zeitschrift für angewandte Mathematik und Physik ZAMP, 1989, 40(2):245-257.
[4] GARAIZAR X. Existence of positive radial solutions for semilinear elliptic equations in the annulus[J]. Journal of Differential Equations, 1987, 70(1):69-92.
[5] LIN Songsun. On the existence of positive radial solutions for nonlinear elliptic equations in annular domains[J]. Journal of Differential Equations, 1989, 81(2):221-233.
[6] HAI D D. Positive solutions to a class of elliptic boundary value problems[J]. Journal of Mathematical Analysis and Applications, 1998, 227(1):195-199.
[7] WANG Haiyan. On the existence of positive solutions for semilinear elliptic equations in the annulus[J]. Journal of Differential Equations, 1994, 109(1):1-7.
[8] ANURADHA V, HAI D D, SHIVAJI R. Existence results for superlinear semipositone BVP[J]. Proceedings of the American Mathematical Society, 1996, 124(3):757-763.
[9] 马如云. 非线性常微分方程非局部问题[M]. 北京:科学出版社, 2004. MA Ruyun. Nonlinear ordinary differential equations of nonlocal problems[M]. Beijing: Science Press, 2004.
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