Positive Solution of Multi-Point Boundary Value Problems for the One-Dimensional p-Laplacian with Singularities期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Positive Solution of Multi-Point Boundary Value Problems for the One-Dimensional p-Laplacian with Singularities

Authors:

Affiliation:

(1) College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, Shandong Province 266510, China;(2) Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China

Abstract:

Abstract In this paper, we obtain positive solution to the following multi-point singular boundary value problem with p-Laplacian operator,

$left{ {begin{array}{*{20}c} {{{left( {phi _{p} {left( {{u}ifmmode{'}else$'$fi} right)}} right)}^{prime } + q{left( t right)}f{left( {t,u,{u}ifmmode{'}else$'$fi} right)} = 0,}} & {{0 < t < 1,}} {{u{left( 0 right)} = {sumlimits_{i = 1}^n {alpha _{i} u{left( {xi _{i} } right)},} }}} & {{{u}ifmmode{'}else$'$fi{left( 1 right)} = {sumlimits_{i = 1}^n {beta _{i} {u}ifmmode{'}else$'$fi{left( {xi _{i} } right)},} }}} end{array} } right.$

where ϕ _p(s) = |s|^p-2 s, p ≥ 2; ξ_i ∈? (0, 1) (i = 1, 2, ··· , n), 0 ≤ α _i, β _i < 1 (i = 1, 2, ··· , n), $phi _{p} {left( s right)} = {left| s right|}^{{p - 2}} s,p geqslant 2;xi _{i} in {left( {0,1} right)}{left( {i = 1,2, cdot cdot cdot ,n} right)},0 leqslant alpha _{i} ,beta _{i} < 1{left( {i = 1,2, cdot cdot cdot ,n} right)},;0 leqslant {sumlimits_{i = 1}^n {alpha _{i} ,{sumlimits_{i = 1}^n {beta _{i} < 1,} }} }$ and q(t) may be singular at t = 0, 1; f(t, u, u′) may be singular at u′ = 0. Supported by the National Natural Science Foundation of China (No. 10371006)

Keywords:

Singularity positive solution p-Laplacian

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