On the existence of positive solutions of integrodifferential equations

Abstract

This paper is concerned with the existence of positive solutions of the integrodifferential equation

,where n is a positive integer and K is a nonnegative continuous function on the interval[0,∞]. More precisely, sufficient conditions are derived for this equation to have positive solutions which tend to zero at ∞. For the special case where n=2, necessary conditions, and necessary and sufficient conditions are obtained for the existence of positive solutions which are bounded at ∞

Keywords:

• Integrodifferential equations
• positive solutions