Existence of a positive solution for a <inline-formula><graphic file="1687-2770-2005-576572-i1.gif"/></inline-formula>-Laplacian semipositone problem

• Main Authors: Shivaji R, Chhetri Maya
• Format: Article
• Language: English
• Published: SpringerOpen 2005-01-01
• Series: Boundary Value Problems
• Online Access: http://www.boundaryvalueproblems.com/content/2005/576572

<p/> <p>We consider the boundary value problem <inline-formula><graphic file="1687-2770-2005-576572-i2.gif"/></inline-formula> in <inline-formula><graphic file="1687-2770-2005-576572-i3.gif"/></inline-formula> satisfying <inline-formula><graphic file="1687-2770-2005-576572-i4.gif"/></inline-formula> on <inline-formula><graphic file="1687-2770-2005-576572-i5.gif"/></inline-formula>, where <inline-formula><graphic file="1687-2770-2005-576572-i6.gif"/></inline-formula> on <inline-formula><graphic file="1687-2770-2005-576572-i7.gif"/></inline-formula>, <inline-formula><graphic file="1687-2770-2005-576572-i8.gif"/></inline-formula> is a parameter, <inline-formula><graphic file="1687-2770-2005-576572-i9.gif"/></inline-formula> is a bounded domain in <inline-formula><graphic file="1687-2770-2005-576572-i10.gif"/></inline-formula> with <inline-formula><graphic file="1687-2770-2005-576572-i11.gif"/></inline-formula> boundary <inline-formula><graphic file="1687-2770-2005-576572-i12.gif"/></inline-formula>, and <inline-formula><graphic file="1687-2770-2005-576572-i13.gif"/></inline-formula> for <inline-formula><graphic file="1687-2770-2005-576572-i14.gif"/></inline-formula>. Here, <inline-formula><graphic file="1687-2770-2005-576572-i15.gif"/></inline-formula> is a <inline-formula><graphic file="1687-2770-2005-576572-i16.gif"/></inline-formula> nondecreasing function for some <inline-formula><graphic file="1687-2770-2005-576572-i17.gif"/></inline-formula> satisfying <inline-formula><graphic file="1687-2770-2005-576572-i18.gif"/></inline-formula> (semipositone). We establish a range of <inline-formula><graphic file="1687-2770-2005-576572-i19.gif"/></inline-formula> for which the above problem has a positive solution when <inline-formula><graphic file="1687-2770-2005-576572-i20.gif"/></inline-formula> satisfies certain additional conditions. We employ the method of subsuper solutions to obtain the result.</p>