Infinite semipositone problems with indefinite weight and asymptotically linear growth forcing-terms

Abstract

In this work, we study the existence of positive solutions to the singular problem $$displaylines{ -Delta_{p}u = lambda m(x)f(u)-u^{-alpha} quad hbox{in }Omega,cr u = 0 quad hbox{on }partial Omega, }$$ where $lambda$ is positive parameter, $Omega $ is a bounded domain with smooth boundary, $ 0 m_0>0$, $|m|_{infty}<infty$. We prove the existence of a positive solution for a certain range of $lambda$ using the method of sub-supersolutions.

Keywords

• Infinite semipositone problem
• indefinite weight
• forcing term
• asymptotically linear growth
• sub-supersolution method