Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Existence and Non-Existence of Positive Solutions of BVPs for Singular ODEs on Whole Lines

  • LIU, YUJI (Department of Mathematics, Guangdong University of Finance and Economics) ;
  • YANG, PINGHUA (Department of Basic Courses, Shijiazhuang Mechanical Engineering College)
  • Received : 2014.05.16
  • Accepted : 2014.09.19
  • Published : 2015.12.23
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Abstract

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $[{\Phi}({\rho}(t)x^{\prime}(t))]^{\prime}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

Keywords

Acknowledgement

Supported by : Natural Science Foundation of Guangdong province, Natural Science Foundation of Hunan province

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