A remark on the nodal regions of the solutions of some superlinear elliptic equations

Abstract

SynopsisWe study the problemwhere Ω is a bounded domain in ℝn(N≧3), 2 <p ≦2N/N – 2, λ ∈R. We prove the existence of nontrivial solutions of (*) for which we can estimate the number of nodal regions dependent on the eigenvalues of −Δ less than λ.