Existence of Positive Solutions to Semipositone Singular Dirichlet Boundary Value Problems  

作　　者：Svatoslav STAN■K 

机构地区：[1]Department of Mathematical Analysis,Faculty of Science,Palack■University

出　　处：《Acta Mathematica Sinica,English Series》2006年第6期1891-1914,共24页数学学报（英文版）

基　　金：This work is supported by Grant No.201/04/1077 of the Grant Agency of Czech Republic;by the Council of Czech Government MSM 6198959214

摘　　要：The paper presents the conditions which guarantee that for some positive value of μ there are positive solutions of the differential equation （Ф（x＇））＇＋μQ（t, x, x＇） = 0 satisfying the Dirichlet boundary conditions x（0） = x（T） = 0. Here Q is a continuous function on the set [0, T] × （0, ∞） ~ （R ／ {0}） of the semipositone type and Q is singular at the value zero of its phase variables.The paper presents the conditions which guarantee that for some positive value of μ there are positive solutions of the differential equation （Ф（x＇））＇＋μQ（t, x, x＇） = 0 satisfying the Dirichlet boundary conditions x（0） = x（T） = 0. Here Q is a continuous function on the set [0, T] × （0, ∞） ~ （R ／ {0}） of the semipositone type and Q is singular at the value zero of its phase variables.

关 键 词：EXISTENCE positive solution semipositone singular problem Dirichlet boundary conditions Ф-Laplacian 

分 类 号：O175.8[理学—数学]