The existence of countably many positive solutions for nonlinear singular m-point boundary value problems on the half-line

In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some p>1, we study the existence of countably many positive solutions for nonlinear boundary value problems on the half-line (@f(u^'))^'+a(t)f(u(t))=0,0R is the increasing homeomorphism and positive homomorphism and @f(0)=0. We show the sufficient conditions for the existence of countably many positive solutions by using the fixed-point index theory and a new fixed-point theorem in cones.

[1]  Bing Liu.  Positive solutions of three-point boundary value problems for the one-dimensional p-laplacian with infinitely many singularities , 2004, Appl. Math. Lett..

[2]  Weigao Ge,et al.  Existence of Three Positive Solutions for Quasi-linear Boundary Value Problem , 2005 .

[3]  E. Kaufmann,et al.  POSITIVE SOLUTIONS OF A THREE-POINT BOUNDARY-VALUE PROBLEM ON A TIME SCALE , 2003 .

[4]  V. Lakshmikantham,et al.  Dynamic systems on measure chains , 1996 .

[5]  Ravi P. Agarwal,et al.  Multiplicity Results for Singular Conjugate, Focal, and (N, P) Problems , 2001 .

[6]  K. Deimling.  Nonlinear functional analysis , 1985 .

[7]  Chuanzhi Bai,et al.  Existence of multiple positive solutions for nonlinear m-point boundary value problems , 2003 .

[8]  Zhang Jihui,et al.  The Method of Lower and Upper Solutions for Fourth-Order Two-Point Boundary Value Problems , 1997 .

[9]  Mirosława Zima,et al.  On Positive Solutions of Boundary Value Problems on the Half-Line , 2001 .

[10]  Hua Su,et al.  The existence of countably many positive solutions for a system of nonlinear singular boundary value problems with the p-Laplacian operator☆ , 2007 .

[11]  Nickolai Kosmatov,et al.  A multiplicity result for a boundary value problem with infinitely many singularities , 2002 .

[12]  Wan-Tong Li,et al.  Eigenvalue problems for second-order nonlinear dynamic equations on time scales , 2006 .

[13]  Qingkai Kong,et al.  Oscillation Theory for Functional Di erential Equations , 1994 .

[14]  Zhimin He.  Double Positive Solutions of Three-Point Boundary Value Problems for p-Laplacian Difference Equations , 2005 .

[15]  J. Baxley,et al.  Existence and uniqueness for nonlinear boundary value problems on infinite intervals , 1990 .

[16]  L. A. Peletier,et al.  Stabilization of solutions of a degenerate nonlinear diffusion problem , 1982 .

[17]  Georges Iffland.  Positive solution of a problem of Emden-Fowler type with a free boundary , 1987 .

[18]  Weigao Ge,et al.  Triple positive solutions for boundary value problems on infinite intervals , 2007 .

[19]  W. Ames,et al.  Nonlinear problems in abstract cones , 1988 .

[20]  Johnny Henderson,et al.  Existence of Solutions for a One Dimensional p-Laplacian on Time-Scales , 2004 .

[21]  Zhimin He,et al.  Double positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales , 2005 .

[22]  Yansheng Liu,et al.  Existence and unboundedness of positive solutions for singular boundary value problems on half-line , 2003, Appl. Math. Comput..

[23]  Baoqiang Yan,et al.  Multiple unbounded solutions of boundary value problems for second-order differential equations on the half-line , 2002 .

[24]  Jihui Zhang,et al.  The existence of positive solutions for some nonlinear boundary value problems with linear mixed boundary conditions , 2005 .

[25]  Wan-Tong Li,et al.  Existence theory for positive solutions to one-dimensional p-Laplacian boundary value problems on time scales , 2007 .

[26]  S. Hilger.  Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus , 1990 .

[27]  Wan-Tong Li,et al.  Nonoscillation and Oscillation Theory for Functional Differential Equations , 2004 .

[28]  R. Leggett,et al.  Multiple positive fixed points of nonlinear operators on ordered Banach spaces , 1979 .

[29]  Jihui Zhang,et al.  The existence of positive solutions for some nonlinear equation systems , 2006 .

[30]  Jianhua Shen,et al.  Existence of three positive solutions for boundary value problems with p-Laplacian ✩ , 2005 .

[31]  Hua Su,et al.  The existence of positive solutions for nonlinear singular boundary value system with p-Laplacian , 2006, Appl. Math. Comput..

[32]  Chuanzhi Bai,et al.  Existence of multiple positive solutions for nonlinear m-point boundary-value problems , 2003, Appl. Math. Comput..

[33]  Ravi P. Agarwal,et al.  Infinite Interval Problems for Differential, Difference and Integral Equations , 2001 .

[34]  Johnny Henderson,et al.  Existence of three positive pseudo-symmetric solutions for a one dimensional p-Laplacian , 2003 .

[35]  Haiyan Wang,et al.  On the existence of positive solutions for semilinear elliptic equations in the annulus , 1994 .

[36]  B. Song,et al.  Controlling wound healing through debridement , 2004, Math. Comput. Model..

[37]  G. Guseinov,et al.  On Green's functions and positive solutions for boundary value problems on time scales , 2002 .

[38]  Shihuang Hong,et al.  Triple positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales , 2007 .

[39]  A. Peterson,et al.  Dynamic Equations on Time Scales: An Introduction with Applications , 2001 .

[40]  Junyu Wang.  The existence of positive solutions for the one-dimensional $p$-Laplacian , 1997 .

[41]  Chengmin Hou,et al.  Existence of multiple positive solutions for one-dimensional p-Laplacian , 2006 .

[42]  Hong‐Rui Sun,et al.  Existence of positive solutions to second-order time scale systems , 2005 .

[43]  Ravi P. Agarwal,et al.  Half-linear dynamic equations , 2003 .

[44]  Ravi P. Agarwal,et al.  Singular Boundary Value Problems for Superlinear Second Order Ordinary and Delay Differential Equations , 1996 .