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Solutions of biharmonic equations with mixed nonlinearity

Research paper by Bin Liu

Indexed on: 08 Nov '14Published on: 08 Nov '14Published in: Boundary Value Problems



Abstract

In this paper, we study the following biharmonic equations with mixed nonlinearity: Δ2u−Δu+V(x)u=f(x,u)+λξ(x)|u|p−2uOpen image in new window, x∈RNOpen image in new window, u∈H2(RN)Open image in new window, where V∈C(RN)Open image in new window, ξ∈L22−p(RN)Open image in new window, 1≤p<2Open image in new window, and λ>0Open image in new window is a parameter. The existence of multiple solutions is obtained via variational methods. Some recent results are improved and extended.MSC: 35J35, 35J60.