Positive solutions to one-dimensional quasilinear impulsive indefinite boundary value problems

Abstract

Abstract Consider the one-dimensional quasilinear impulsive boundary value problem involving the p-Laplace operator {−(ϕp(u′))′=λω(t)f(u),00 $\lambda, \mu >0$ are two positive parameters, ϕp(s) $\phi_{p}(s)$ is the p-Laplace operator, i.e., ϕp(s)=|s|p−2s $\phi_{p}(s)=|s|^{p-2}s$, p>1 $p>1$, ω(t) $\omega (t)$ changes sign on [0,1] $[0,1]$. Several new results are obtained for the above quasilinear indefinite problem.

Keywords

• Multiplicity of positive solutions
• Indefinite weight function
• p-Laplace operator
• Quasilinear impulsive differential equation