A Lyapunov-type inequality for a ψψ-Laplacian operator

We prove a Lyapunov-type inequality for a ψψ-Laplacian operator where ψψ is an odd increasing function which is sub-multiplicative on [0,∞)[0,∞) and Ψ(s)=1ψ(s) is a convex function for s>0s>0. From this inequality we easily derive some previous results on the number of zeros, nodal domains and bounds on eigenvalues of nontrivial solutions for certain boundary value problems including the pp-Laplacian. Our method of proof does not require the standard approach via classical Jensen, Cauchy–Schwarz and Hölder inequalities.