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| Titel: |
Positive Solutions to Semilinear Elliptic Equations with Logistic Type Nonlinearities and Constant Yield Harvesting in N |
| Auteur: |
Costa, David G. Drabek, Pavel Tehrani, Hossein T. |
| Verschenen in: |
Communications in partial differential equations |
| Paginering: | Jaargang 33 (2008) nr. 9 pagina's 1597-1610 |
| Jaar: |
2008-09 |
| Inhoud: |
We consider a class of semilinear elliptic equations - Δ u = f(x, u) in all of N with nonlinearities of the form [image omitted] where λ, μ are positive parameters, a(x), h(x) are positive functions, and g(u) is a super-linearly increasing function in a more general fashion than the classical logistic term u2. From a practical point of view, these problems can provide models for fishery or hunting management (cf. [8]) where μ h(x) denotes a harvesting term and, as such, one is interested in situations allowing the existence of positive solutions. From a mathematical point of view, these elliptic problems belong to the class of so-called semi-positone problems (cf. [2]) because the nonlinearity f(x, u) satisfies f(x, 0) < 0. Under suitable assumptions on a(x), h(x), we use variational methods to show that, for each λ > λ1 (a) (where λ1 (a) denotes the principal eigenvalue of - Δ u = λ a(x)u ∈ D1,2(N)), there exists a positive solution decaying at infinity like O(|x|-(N-2)), provided that 0 < μ < [image omitted](λ). |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 50 van 69 gevonden artikelen
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