Positive stationary solutions of convection-diffusion equations for superlinear sources

• Autorzy: Orpel Aleksandra

Identyfikatory

DOI

10.7494/OpMath.2022.42.5.727

• Języki publikacji: EN

Abstrakty

EN

We investigate the existence and multiplicity of positive stationary solutions for a certain class of convection-diffusion equations in exterior domains. This problem leads to the following elliptic equation Δu(x) + f(x, u(x)) + g(x)x · ∇u(x) = 0, for x ∈ ΩR = {x ∈ Rn, ∥x∥ > R}, n > 2. The goal of this paper is to show that our problem possesses an uncountable number of nondecreasing sequences of minimal solutions with finite energy in a neighborhood of infinity. We also prove that each of these sequences generates another solution of the problem. The case when f(x, ·) may be negative at the origin, so-called semipositone problem, is also considered. Our results are based on a certain iteration schema in which we apply the sub and supersolution method developed by Noussair and Swanson. The approach allows us to consider superlinear problems with convection terms containing functional coefficient g without radial symmetry.

Słowa kluczowe

EN

semipositone problems; positive stationary solutions; minimal solutions with finite energy; sub and supersolutions methods

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2022
• Tom: Vol. 42, no. 5
• Strony: 727--749
• Opis fizyczny: Bibliogr. 33 poz.

Twórcy

autor

Orpel Aleksandra

• University of Lodz, Faculty of Mathematics and Computer Science, S. Banacha 22, 90-238 Lodz, Poland

• https://orcid.org/0000-0001-8360-7083

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).