Picone’s identity for -Laplace operator and its applications

UDC 517.9 We study the existence of multiple solutions for the biharmonic problem Δ 2 u = f ( x , u ) + g ( x , u ) in Ω , u = ∂ ν u = 0 on ∂ Ω , where Ω is a bounded domain with smooth boundary in ℝ N , N > 4 , f ( x , ξ ) is odd in ξ , and g ( x , ξ ) is a perturbation term. Under certain growth conditions on f and g , we show that there are infinitely many weak solutions to the problem.

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Picone’s identity for -Laplace operator and its applications

Abstract: UDC 517.9We prove a nonlinear analogue of Picone's identity for -Laplace operator. As an application, we give a Hardy type inequality and Sturmian comparison principle.We also show the strict monotonicity of the principle eigenvalue and degenerate elliptic system.

Cited by 2 publications

References 21 publications

Multiple Solutions to Boundary-Value Problems for Fourth-Order Elliptic Equations

Multiple Solutions to Boundary-Value Problems for Fourth-Order Elliptic Equations

Multiple solutions to boundary-value problems for fourth-order elliptic equations

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