On an asymptotically pp-linear pp-Laplacian equation in RNRN

In this paper, we study the existence of positive solutions and sign-changing solutions for the pp-Laplacian equation −Δpu+λg(x)∣u∣p−2u=f(x,u),x∈RN, where λλ is a positive parameter and the nonlinear term ff is superlinear at zero and asymptotically pp-linear at infinity.