Multiplicity results for a class of superlinear elliptic problems

Costa, David; Wang, Zhi-Qiang

doi:10.1090/S0002-9939-04-07635-X

Multiplicity results for a class of superlinear elliptic problems
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by David G. Costa and Zhi-Qiang Wang PDF

Proc. Amer. Math. Soc. 133 (2005), 787-794 Request permission

Abstract:

We study a class of superlinear elliptic problems $-\Delta u = \lambda f(u)$ under the Dirichlet boundary condition on a bounded smooth domain in $\mathbb R^N$. Assuming that the nonlinearity $f(u)$ is superlinear in a neighborhood of $u=0$, we study the dependence of the number of signed and sign-changing solutions on the parameter $\lambda$.

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