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

Previous Articles     Next Articles

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

PDF (PC)

582

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.
[1] SHEN Liu-xiao, ZHAO Chun. Optimal control for inputting rate of a size-structure competitive system [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(7): 21-29.
[2] CAO Xue-jing, LUO Zhi-xue. Optimal control of forest evolution system in polluted environment [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(7): 15-20.
[3] ZHANG Sha, JIA Mei, LI Yan, LI Xiao-chen. Existence and uniqueness of solutions for three point boundary value problems of impulsive fractional differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 66-72.
[4] FENG Hai-xing, ZHAI Cheng-bo. Multiple positive solutions of a system of high order nonlinear fractional differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 48-57.
[5] RONG Wen-ping, CUI Jing. μ-pseudo almost automorphic solutions for a class of stochastic evolution equations under non-Lipschitz conditions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 64-71.
[6] CHEN Bin. Third-order periodic boundary value problems with sign-changing Greens function [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 79-83.
[7] WU Cheng-ming. Existence of positive periodic solutions for second order singular coupled systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(10): 81-88.
[8] CHEN Qiang, JIA Mei, ZHANG Hai-bin. Existence and uniqueness of solutions for nonlinear fractional four-point boundary value problems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 42-48.
[9] YANG Hao, LIU Xi-ping, WU Gui-yun. Existence of the solutions for a type of nonlocal boundary value problems for fractional differential equations with p-Laplacian operator [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 56-62.
[10] ZHENG Chun-hua, LIU Wen-bin. Existence of positive solutions of the boundary value problem for a class of fractional differential equations with delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(03): 73-79.
[11] YANG Xue-jie, SUN Guo-zheng*, CHEN Wen. Shock solution for a quasilinear singularly perturbed problem#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(04): 79-83.
[12] ZHANG Lu, MA Ru-yun. Bifurcation structure of asymptotically linear second-order #br# semipositone discrete boundary value problem#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 79-83.
[13] ZHOU Wen-xue1,2, LIU Hai-zhong1. Existence of solution for the  boundary value problem of a class of fractional differential equation [J]. J4, 2013, 48(8): 45-49.
[14] QIN Xiao-na, JIA Mei*, LIU Shuai. Existence of positive solutions for fractional differential equations boundary value problems with Caputo derivative [J]. J4, 2013, 48(10): 62-67.
[15] ZHANG Hai-yan1,2, LI Yao-hong2. ositive solutions of boundary value problems for systems of nonlinear mixed higher order singular differential equations [J]. J4, 2012, 47(2): 31-35.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd