Abstract
We use the Morawetz multiplier to show that there are no nontrivial solutions of certain decay order for a biharmonic equation with a p-Laplacian term and a system of coupled biharmonic equations with p-Laplacian terms in the entire Euclidean space.
Highlights
Http://creativecommons.org/licenses/by/4.0/ Recently, there has been an active research on the biharmonic equation with a
We shall use the Morawetz multiplier [43] [44] [45] to show that there are no nontrivial solutions of certain decay order for (1.1)
( ) Since u and v ∈ Ds,[3] Rn , u ≡ 0 and v ≡ 0
Summary
As well as the evolutionary biharmonic equations with a p-Laplacian term ( ) ∂u ∂t = ∆2u + α∇ ⋅ ∇u p−2 ∇u + β ⋅ u + f ( x,u). We shall use the Morawetz multiplier [43] [44] [45] to show that there are no nontrivial solutions of certain decay order for (1.1). The subscript denotes the partial derivative, us =∂u ∂s. Ck Rn is the space of functions whose partial derivatives of order up to and including k are continuously differentiable. A function u is said to be of decay order (h, k) if and only if ( ) u ∈ Dh,k Rn. All the functions are assumed to be real-valued
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