Multiple Solutions of Quasilinear Elliptic Equations in ℝ𝑁 - Huei-li Lin (International Journal of Differential Equations)
Assume that 𝑄 is a positive continuous function in ℝ𝑁 and satisfies some suitable conditions. We prove that the quasilinear elliptic equation −Δ𝑝𝑢+|𝑢|𝑝−2𝑢=𝑄(𝑧)|𝑢|𝑞−2𝑢 in ℝ𝑁 admits at least two solutions in ℝ𝑁 (one is a positive ground-state solution and the other is a sign-changing solution).