p-Laplacian Equations in ℝN with Finite Potential via the Truncation Method

Abstract

We consider the problem -Δp⁢u+a⁢(x)⁢|u|p-2⁢u=|u|q-2⁢u{-\Delta_{p}u+a(x)\lvert u\rvert^{p-2}u=\lvert u\rvert^{q-2}u} in ℝN{\mathbb{R}^{N}}, where 1<p<N{1<p<N}, p<q<p*=N⁢pN-p{p<q<p^{*}=\frac{Np}{N-p}}, Δp{\Delta_{p}} is the p-Laplacian operator, and the potential function a is positive, bounded and verifies suitable decay assumptions. The existence of infinitely many solutions of the equation is proved via the truncation method.

Keywords

• finite potential
• multiple solutions
• truncation method
• 35b05
• 35b45