The Positive Solution for Singular Eigenvalue Problem of One-dimensional p-Laplace Operator

In this paper, by constructing a special cone and using
fixed point theorem and fixed point index theorem of cone, we get the
existence of positive solution for a class of singular eigenvalue value
problems with p-Laplace operator, which improved and generalized
the result of related paper.


Authors:



References:
<p>[1] Su H, Wei Z L, Wang B H. The existence of positive solutions four a
nonlinear four-point singular boundary value problem with a p-Laplace
operator. Nonlinear anal,2007,66:2204-2217.
[2] Ma D x, Han J X,Chen X G. Positive solution of boundary value
problem for one-dimensional p-Laplacian with singularities.J Math Anal
Appl,2006,324:118-133.
[3] Liu Y J, Ge W G.Multiple positive solutions to a three-point boundary
value problems with p-Laplacian. J Math Anal Appl,2003,277:293-302
[4] Jin J X, Yin C H.Positive solutions for the boundary value problems
of one-dimensional p-Laplacian with delay. J Math Anal Appl, 2007,
330:1238-1248.
[5] Su H, Wei Z L, Wang B H. The existence of positive solutions four a
nonlinear four-point singular boundary value problem with a p-Laplace
operator. Nonlinear anal,2007,66:2204-2217.
[6] Ma D x, Han J X,Chen X G. Positive solution of boundary value
problem for one-dimensional p-Laplacian with singularities.J Math Anal
Appl,2006,324:118-133.
[7] Sun Y P. Optimal existence criteria for symmetric positive solutions a
three-point boundary differential equations. Nonlinear anal,2007,66:1051-
1063
[8] Tian Yuansheng Liu Chungen. The existence of symmetric positive
solutions for a three-point singular boundary value problem with a p-
Laplace operator.Acta Mathematica scientia 2010,30A(3):784-792.
[9] Xie Shengli. Positive solutions of multiple-point boundary value problems
for systems of nonlinear second order differential equations .Acta
Mathematica scientia 2010,30(A):258-266.
[10] Youyu Wang Weigao Ge Triple positive solutions for two-point
boundary-value problems with one-dimensional p-Laplacian Applicable
analysis 2005 84:821-831
[11] K.Deimling.Nonlinear Functional Analysis, Spring-Verlag,1985.
[12] Guo Dajun Nonlinear functional analysis. Jinan. Shandong science and
technology publishing house,2001 .</p>