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Nonexistence of weak solutions of quasilinear elliptic equations with variable coefficients

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  • In this paper, we are concerned with the following quasilinear elliptic equations:

    -div${a(x)|\nabla u|^{p-2}\nabla u$  $=b(x)|u|^(q-2)u $     in $\Omega$
    $u(x)$   $= 0$ on $\partial\Omega$

    where $\Omega$ is a domain in $\mathbf R^N$ $(N \ge 1)$ with smooth boundary.
          When $a$ and $b$ are positive constants, there are many results on the nonexistence of nontrivial solutions for the equation (E).     The main purpose of this paper is to discuss the nonexistence results for (E) with a class of weak solutions under some assumptions on $a$ and $b$.

    Mathematics Subject Classification: Primary: 35J25; Secondary: 35J20, 35J70.


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