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Two-bubble nodal solutions for slightly subcritical fractional Laplacian. (Chinese. English summary) Zbl 1374.35054

Summary: In this paper, we consider the existence of nodal solutions with two bubbles to the slightly subcritical problem with the fractional Laplacian \[ \begin{cases} (-\Delta)^su=|u|^{p-1-\varepsilon}u,& x\in\Omega,\\u=0, & x\in\partial\Omega,\end{cases} \] where \(\Omega\) is a smooth bounded domain in \(\mathbb{R}^N, N > 2s, 0 < s < 1\), \(p = \frac{N+2s}{N-2s}\) and \(\varepsilon > 0\) is a small parameter.

MSC:

35B33 Critical exponents in context of PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35R11 Fractional partial differential equations
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