In this article we prove the nonlinear analogue of Picone's identity for p−biharmonic operator. As an application of our result we show that the Morse index of the zero solution to a p−biharmonic boundary value problem is 0. We also prove a Hardy type inequality and Sturmian comparison principle. We also show the strict monotonicity of the principle eigenvalue and linear relationship between the solutions of a system of singular p-biharmonic system.
In this article, we obtain several interesting remarks on the qualitative questions such as stability criteria, Morse index, Picone's identity for biharmonic equations.
Abstract. The goal of this paper is to establish singular Adams type inequality for biharmonic operator on Heisenberg group. As an application, we establish the existence of a solution toThe special feature of this problem is that it contains an exponential nonlinearity and singular potential.
Abstract. In this article we deal with the existence questions to the nonlinear biharmonic systems. Using theory of monotone operators, we show the existence of a unique weak solution to the weighted biharmonic systems. We also show the existence of a positive solution to weighted biharmonic systems in the unit ball in R n , using Leray Schauder fixed point theorem. In this study we allow sign-changing weights.Mathematics subject classification (2010): 35J08, 35J58, 35J60, 35J75, 35J91.
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