On a singular nonlinear semilinear elliptic problem

1998 ◽  
Vol 128 (6) ◽  
pp. 1389-1401 ◽  
Author(s):  
Junping Shi ◽  
Miaoxin Yao
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Image Position

We consider the singular boundary value problemWe study the existence, uniqueness, regularity and the dependency on parameters of the positive solutions under various assumptions.

Existence of solutions in a singular biharmonic nonlinear problem

1993 ◽  
Vol 36 (3) ◽  
pp. 537-546 ◽  
Author(s):  
Gaston L. Hernandez ◽  
Y. Choi
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Nonlinear Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Image Position

In this work we prove the existence and uniqueness of positive solutions of the nonlinear singular boundary value problemwhere 0<σ<1.Extensions of the above results to the case of Δ2u−f(x, u) = 0 with appropriate singularity built into f are also given.

scholarly journals Positive Solutions of Nonresonant Singular Boundary Value Problem of Second Order Differential Equations

2001 ◽  
Vol 162 ◽  
pp. 127-148 ◽  
Author(s):  
Zhongli Wei ◽  
Changci Pang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Second Order Differential Equations ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient

This paper investigates the existence of positive solutions of nonresonant singular boundary value problem of second order differential equations. A necessary and sufficient condition for the existence of C[0, 1] positive solutions as well as C1[0, 1] positive solutions is given by means of the method of lower and upper solutions with the fixed point theorems.

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