## Existence of changing sign solutions for some semilinear problems with jumping nonlinearities at zero.(English)Zbl 0819.35054

Let $h(u)= \begin{cases} au- \alpha u^ 2, &u\geq 0\\ du+ \beta u^ 2, &u\leq 0 \end{cases},$ where $$\alpha\geq 0$$, $$\beta>0$$ and $$a,d> \lambda_ 1$$, here $$\lambda_ 1$$ denotes the first eigenvalue of $$-\Delta$$ under zero Dirichlet data on a bounded smooth domain $$D$$ in $$\mathbb{R}^ n$$. A domain in the $$ad$$-plane is found to characterize the existence of changing sign solutions of the equation $$-\Delta u= h(u)$$, $$u|_{\partial D}=0$$.

### MSC:

 35J65 Nonlinear boundary value problems for linear elliptic equations 35J20 Variational methods for second-order elliptic equations 35R05 PDEs with low regular coefficients and/or low regular data
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### References:

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