Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 36, pp. 114.
Positive solutions for a 2nthorder pLaplacian boundary
value problem involving all derivatives
Youzheng Ding, Jiafa Xu, Xiaoyan Zhang
Abstract:
In this work, we are mainly concerned with the positive
solutions for the 2nthorder pLaplacian boundaryvalue
problem
where
and
.
To overcome the difficulty resulting from all derivatives,
we first convert the above problem into a boundary value problem
for an associated second order integroordinary differential equation
with pLaplacian operator. Then, by virtue of the classic fixed
point index theory, combined with a priori estimates of positive solutions,
we establish some results on the existence and multiplicity of positive
solutions for the above problem. Furthermore, our nonlinear term f is
allowed to grow superlinearly and sublinearly.
Submitted September 10, 2012. Published January 30, 2013.
Math Subject Classifications: 34B18, 45J05, 47H1.
Key Words: Integroordinary differential equation; a priori estimate;
index; fixed point; positive solution.
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Youzheng Ding
School of Mathematics, Shandong University
Jinan 250100, Shandong, China
email: dingyouzheng@139.com


Jiafa Xu
School of Mathematics, Shandong University
Jinan 250100, Shandong, China
email: xujiafa292@sina.com


Xiaoyan Zhang
School of Mathematics, Shandong University
Jinan 250100, Shandong, China
email: zxysd@sdu.edu.cn

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