Nonnegative entire bounded solutions to some semilinear equations involving the fractional Laplacian
The main goal is to establish necessary and sufficient conditions under which the fractional semilinear elliptic equation $\Delta^{\frac{\alpha}{2}} u=\rho(x)\,\varphi(u)$ admits nonnegative nontrivial bounded solutions in the whole space $\mathbb{R}^N$.
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | The main goal is to establish necessary and sufficient conditions under which
the fractional semilinear elliptic equation $\Delta^{\frac{\alpha}{2}}
u=\rho(x)\,\varphi(u)$ admits nonnegative nontrivial bounded solutions in the
whole space $\mathbb{R}^N$. |
|---|---|
| DOI: | 10.48550/arxiv.1506.08294 |