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This article is cited in 4 scientific papers (total in 4 papers)
On existence of nodal solution to elliptic equations with convex-concave nonlinearities
V. E. Bobkov Institute of Mathematics CS USC RAS, Chernyshevskii str., 112,
450008, Ufa, Russia
Abstract:
In a bounded connected domain $\Omega \subset \mathbb{R}^N$, $N \geqslant 1$, with a smooth boundary, we consider the Dirichlet boundary value problem for elliptic equation with a convex-concave nonlinearity
\begin{equation*}
\begin{cases}
-\Delta u = \lambda |u|^{q-2} u + |u|^{\gamma-2} u, \quad x \in \Omega \\ u|_{\partial \Omega} = 0,
\end{cases}
\end{equation*}
where $1< q< 2< \gamma < 2^*$. As a main result, we prove the existence of a nodal solution to this equation on the nonlocal interval $\lambda \in (-\infty, \lambda_0^*)$, where $\lambda_0^*$ is determined by the variational principle of nonlinear spectral analysis via fibering method.
Keywords:
nodal solution, convex-concave nonlinearity, fibering method.
Received: 05.03.2012
Citation:
V. E. Bobkov, “On existence of nodal solution to elliptic equations with convex-concave nonlinearities”, Ufimsk. Mat. Zh., 5:2 (2013), 18–30; Ufa Math. J., 5:2 (2013), 18–30
Linking options:
https://www.mathnet.ru/eng/ufa195https://doi.org/10.13108/2013-5-2-18 https://www.mathnet.ru/eng/ufa/v5/i2/p18
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Abstract page: | 378 | Russian version PDF: | 121 | English version PDF: | 12 | References: | 78 | First page: | 2 |
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