Multiple positive solutions for some p-Laplacian boundary value problems

This paper deals with the existence of multiple positive solutions for the one-dimensional p-Laplacian(@f"p(x^'(t)))^'+q(t)f(t,x(t),x^'(t))=0,t@?(0,1)subject to the following boundary value conditions:x(0)=@?i=1n@a"ix(@x"i),x(1)=@?i=1n@b"ix(@x"i),where @f"p(s)=|s|^p^-^2.s, p>1. By means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of at least three positive solutions to the above boundary value problem.

[1]  P. Ubilla,et al.  Multiplicity Results for the 1-Dimensional Generalized p-Laplacian , 1995 .

[2]  Manuel del Pino,et al.  A homotopic deformation along p of a Leray-Schauder degree result and existence for (¦u′¦p − 2u′)′ + ƒ(t, u) = 0, u(0) = u(T) = 0, p > 1 , 1989 .

[3]  Donal O'Regan,et al.  Multiple positive solutions for the one-dimensional singular p-Laplacian , 2002, Appl. Math. Comput..

[4]  Junyu Wang,et al.  Multiple positive solutions for the one-dimensional p -Laplacian , 2000 .

[5]  Ravi P. Agarwal,et al.  Eigenvalues and the One-Dimensional p-Laplacian☆☆☆ , 2002 .

[6]  Zhanbing Bai,et al.  Multiple positive solutions for some p-Laplacian boundary value problems☆ , 2004 .

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

[8]  Weigao Ge,et al.  Existence of three solutions for a quasilinear two-point boundary value problem , 2003 .

[9]  Allan Peterson,et al.  Three positive fixed points of nonlinear operators on ordered banach spaces , 2001 .

[10]  Weigao Ge,et al.  Existence and iteration of monotone positive solutions for multipoint boundary value problem with p-Laplacian operator , 2005 .

[11]  D. O’Regan,et al.  Positive Solutions of Differential, Difference and Integral Equations , 1998 .

[12]  Jihui Zhang,et al.  Positive solutions for one-dimensional p-Laplacian boundary value problems with dependence on the first order derivative , 2006 .

[13]  Weigao Ge,et al.  Multiple positive solutions for one-dimensional p-Laplacian boundary value problems , 2002, Appl. Math. Lett..

[14]  Fu-Hsiang Wong,et al.  Existence of positive solutions for m-Laplacian boundary value problems , 1999 .

[15]  Roberto Livrea.  Existence of three solutions for a quasilinear two point boundary value problem , 2002 .

[16]  Donal O'Regan,et al.  Some general existence principles and results for f y ′ =qf t,y,y ′ ,0 , 1993 .

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

[18]  Chengkui Zhong,et al.  A note on singular nonlinear boundary value problems for the one-dimensional p-Laplacian , 2001, Appl. Math. Lett..