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| In this paper, we consider a nonlinear elliptic equation driven by
the $p$-Laplacian and with a parameter $\lambda>0$. Using a
combination of variational and degree theoretic methods, we show
that there exists $\lambda^*>0$ such that, if $\lambda>\lambda^*,$
then the problem has two positive smooth solutions. Our result
extends earlier ones by Rabinowitz (semilinear equations) and Guo
(nonlinear equations) |
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