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Picone’s identity for biharmonic operators on Heisenberg group and its applications. (English) Zbl 1381.35199

Summary: In this paper, we establish a nonlinear analogue of Picone’s identity for biharmonic operators on Heisenberg group. As an applications of Picone’s identity, we obtain Hardy-Rellich type inequality, Morse index, Caccioppoli inequality, Picone inequality for biharmonic operators on Heisenberg group.

MSC:

35R03 PDEs on Heisenberg groups, Lie groups, Carnot groups, etc.
35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
35B35 Stability in context of PDEs
35J30 Higher-order elliptic equations
35R45 Partial differential inequalities and systems of partial differential inequalities
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