A Counterexample for Singular Equations with Indefinite Weight

Abstract

We construct a second-order equation x¨=h⁢(t)/xp{\ddot{x}=h(t)/x^{p}}, with p>1{p>1} and the sign-changing, periodic weight function h having negative mean, which does not have periodic solutions. This contrasts with earlier results which state that, in many cases, such periodic problems are solvable.

Keywords

• periodic solutions
• singular equations
• indefinite weight
• 34b15
• 34b16