Existence of nonminimal solutions to an inhomogeneous elliptic equation with supercritical nonlinearity
| Autor: | Ishige Kazuhiro, Okabe Shinya, Sato Tokushi |
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| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Advanced Nonlinear Studies, Vol 23, Iss 1, Pp 63-95 (2023) |
| Druh dokumentu: | article |
| ISSN: | 2169-0375 2022-0073 |
| DOI: | 10.1515/ans-2022-0073 |
| Popis: | In our previous paper [K. Ishige, S. Okabe, and T. Sato, A supercritical scalar field equation with a forcing term, J. Math. Pures Appl. 128 (2019), pp. 183–212], we proved the existence of a threshold κ∗>0{\kappa }^{\ast }\gt 0 such that the elliptic problem for an inhomogeneous elliptic equation −Δu+u=up+κμ-\Delta u+u={u}^{p}+\kappa \mu in RN{{\bf{R}}}^{N} possesses a positive minimal solution decaying at the space infinity if and only if 01p\gt 1 is in the Joseph-Lundgren subcritical case. In this article, we prove the existence of nonminimal positive solutions to the elliptic problem. Our arguments are also applicable to inhomogeneous semilinear elliptic equations with exponential nonlinearity. |
| Databáze: | Directory of Open Access Journals |
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