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Strong unique continuation of eigenfunctions for \(p\)-Laplacian operator. (English) Zbl 0972.35035

Summary: We show the strong unique continuation property of the eigenfunctions for \(p\)-Laplacian operator in the case \(p< N\), i.e. this paper is primarily concerned with the problem: \[ -\text{div}(|\nabla u|^{p- 2}\nabla u)+V|u|^{p- 2}u= 0\quad\text{in }\Omega, \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) and the weight function \(V\) is assumed to be not equivalent to zero and to lie in \(L^{N/p}(\Omega)\).

MSC:

35J60 Nonlinear elliptic equations
35B60 Continuation and prolongation of solutions to PDEs
35J15 Second-order elliptic equations
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
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