Multiplicity of positive solutions of superlinear semi-positone singular Neumann problems

详细信息    查看全文

• 作者：Qiuyue Li (1)
  Fuzhong Cong (1)
  Zhe Li (2)
  Jinkai Lv (1)
  
  1. Department of Foundation Courses ; Aviation University of Airforce ; Renmin Street 7855 ; Changchun ; 130012 ; China
  2. Department of Aviation Mechanical Engineering ; Aviation University of Airforce ; Nanhu Road 2222 ; Changchun ; 130012 ; China
  
• 关键词：positive solutions ; superlinear ; semi ; positone ; singular ; Neumann problem
• 刊名：Boundary Value Problems
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：1,185 KB
• 参考文献：1. Hwang, B, Lee, S, Kim, Y (2014) Existence of an unbounded branch of the set of solutions for Neumann problems involving the p ( x ) $p(x)$ -Laplacian. Bound. Value Probl. 2014: CrossRef
  2. Chu, J, Jiang, D (2005) Multiplicity of positive solutions to second order differential equations with Neumann boundary conditions. Appl. Math. 32: pp. 203-303
  3. Dong, Y (2002) A Neumann problem at resonance with the nonlinearity restricted in one direction. Nonlinear Anal. 51: pp. 739-747 CrossRef
  4. Li, X, Jiang, D (2004) Optimal existence theory for single and multiple positive solutions to second order Neumann boundary value problems. Indian J. Pure Appl. Math. 35: pp. 573-586
  5. Sun, J, Li, W (2003) Multiple positive solutions to second order Neumann boundary value problems. Appl. Math. Comput. 146: pp. 187-194 CrossRef
  6. Lian, H, Zhao, J, Agarwal, R (2014) Upper and lower solution method for nth-order BVPs on an infinite interval. Bound. Value Probl. 2014: CrossRef
  7. Li, Q, Cong, F, Jang, D (2008) Multiplicity of positive solutions to second order Neumann boundary value problems with impulse actions. Appl. Math. Comput. 206: pp. 810-817 CrossRef
  8. Guo, K, Sun, J, Liu, Z (1995) Nonlinear Ordinary Differential Equations Functional Technologies. Shan Dong Science Technology, Shan Dong
  9. Deimling, K (1985) Nonlinear Functional Analysis. Springer, New York CrossRef
  
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

Introduction Neumann boundary value problems have been studied by many authors. We are mainly interested in the semi-positone case. This paper deals with the existence and multiplicity of positive solutions of a superlinear semi-positone singular Neumann boundary value problem. Preliminaries The proof of our main results relies on a nonlinear alternative of Leray-Schauder type, the method of upper and lower solutions and on a well-known fixed point theorem in cones. Main results We obtained the existence of at least two different positive solutions.