LAUSR

In this work, we investigate the (2, p)-Laplacian equation −Δu − Δpu = f(x, u) in Ω with the boundary condition u = 0 on ∂Ω, where Ω is a smooth bounded domain in RN, p > 2, and the nonlinearity f has extension property at both the zero and infinity points. We observe that the above equation admits at least two positive solutions, owing to the mountain pass theorem and Ekeland’s variational principle.In this work, we investigate the (2, p)-Laplacian equation −Δu − Δpu = f(x, u) in Ω with the boundary condition u = 0 on ∂Ω, where Ω is a smooth bounded domain in RN, p > 2, and the nonlinearity f has extension property at both the zero and infinity points. We observe that the above equation admits at least two positive solutions, owing to the mountain pass theorem and Ekeland’s variational principle.