J4

• Articles • Previous Articles    

Existence of positive solutions for singular superlinear threepoint boundary value problems of second order ordinary differential equations

SHEN Wen-guo1 and SONG Lan-an2   

  1. 1． The Basic Course Department of Lanzhou Polytechnic College, Lanzhou 730050, Gansu, China；2． The Library of Lanzhou Polytechnic College, Lanzhou 730050, Gansu, China
  • Received:2006-10-23 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
  • Contact: SHEN Wen-guo

PDF (PC)

1674

Abstract: By means of the fixed point theorem on cons, a necessary and sufficient condition for the existence of C［0,1］ positive solutions are given to singular boundary value problems of a class of second order threepoint superlinear differential equations x″(t)+f(t,x(t))=0, t∈(0,1), x(0)=0, x(1)=kx(η). Where η∈(0,1) is a constant, f∈C((0,1)×［0,∞),［0,∞)).

Key words: fixedpoint theorem on cons , positive solution, singular threepoint boundary value problem, superlinear

CLC Number: 

  • O175.8
[1] WANG Jun-fang, ZHAO Pei-hao. Comparison principles for viscosity solution of fully nonlinear parabolic equations with superlinear gradient nonlinearities [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(8): 77-83.
[2] . Existence of positive solutions for a class of nonlinear second-order Dirichlet problem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 64-69.
[3] YAN Dong-liang. Positive solutions of a second order periodic problems with derivative terms [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(9): 69-75.
[4] LI Tao-tao. Existence of radial positive solutions of second-order semi-positone elliptic differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 48-55.
[5] 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.
[6] GUO Li-jun. Existence of positive solutions for a third-order three-point boundary value problem of nonlinear differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 47-53.
[7] YANG Wen-bin, LI Yan-ling. Dynamics research in a predator-prey system with a nonlinear growth rate [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(03): 80-87.
[8] SUN Yan-mei. Existence of positive solutions for singular fractional #br# differential equations boundary value problems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(2): 71-75.
[9] ZHANG Shen-gui. Multiplicity of solutions for local superlinear p-kirchhoff-type equation#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(05): 61-68.
[10] 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.
[11] 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.
[12] YAO Qing-liu. Existence of a positive solution of singular nonautonomous third-order two-point boundary value problems [J]. J4, 2012, 47(6): 10-15.
[13] FAN Jin-jun, ZHANG Xue-ling, LIU Yan-sheng. Existence of positive solutions of the m-point boundary value problem with p-Laplace operator on time scales [J]. J4, 2012, 47(6): 16-19.
[14] LU Fang, ZHOU Zong-fu*. The existence of positive solutions of  a class of fourth-order singular boundary value problems with a p-Laplacian operator [J]. J4, 2012, 47(6): 28-33.
[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