MAXIMUM PRINCIPLE AND NONLINEAR THREE POINT SINGULAR BOUNDARY VALUE PROBLEMS ARISING DUE TO SPHERICAL SYMMETRY

AMIT K. VERMA; MANDEEP SINGH

Title	MAXIMUM PRINCIPLE AND NONLINEAR THREE POINT SINGULAR BOUNDARY VALUE PROBLEMS ARISING DUE TO SPHERICAL SYMMETRY
Publication Type	Journal Article
Year of Publication	2015
Authors	VERMA, AMITK, SINGH, MANDEEP
Volume	19
Issue	2
Start Page	175
Pagination	15
Date Published	2015
ISSN	1083-2564
AMS	34B16. 34B27, 34B60
Abstract	We consider the following class of nonlinear three point singular boundary value problems (SBVPs) $${ −y ′′(x) −\frac{2}{x} y ′ (x) = f(x, y), \ \ \ \ 0 < x < 1, }$$ $${ y ′ (0) = 0, \ \ \ \ y(1) = δy(η), }$$ where ${ δ > 0 }$ and ${ 0 < η < 1}$. We establish some new maximum principles. Further using these maximum principles and monotone iterative technique in the presence of upper and lower solution we prove existence of solutions for the above class of nonlinear three point SBVPs. Here the nonlinear term is one sided Lipschitz continuous in its domain, also ${ x = 0 }$ is regular singular point of the above differential equation
URL	http://www.acadsol.eu/en/articles/19/2/2.pdf
Refereed Designation	Refereed
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