## 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

### Keywords:

strong unique continuation; $$p$$-Laplacian
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