Ambrosetti-Prodi problem with degenerate potential and Neumann boundary condition

Repovš, Dušan (avtor)

We study the degenerate elliptic equation $$ -\operatorname{div}(|x|^\alpha \nabla u) = f(u) + t\phi(x) + h(x)$$ in a bounded open set $\Omega$ with homogeneous Neumann boundary condition, where $\alpha \in (0,2)$ and $f$ has a linear growth. The main result establishes the existence of real numbers and $t^\ast$ such that the problem has at least two solutions if $t \leq t_\ast$, there is at least one solution if $t_\ast < t \leq t^\ast$, and no solution exists for all $t > t^\ast$. The proof combines a priori estimates with topological degree arguments.

• Jezik: Angleški jezik
• Ključne besede: Ambrosetti-Prodi problem, degenerate potential, topological degree, anisotropic continuous media
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2018
• Št. strani: art. no. 41, str. 1-10
• Številčenje: Vol. 2018
• PID: 20.500.12556/RUL-109446
• UDK: 517.956
• ISSN pri članku: 1072-6691
• COBISS.SI-ID: 18249305
• Datum objave v RUL: 03.09.2019

REPOVŠ, Dušan, 2018, Ambrosetti-Prodi problem with degenerate potential and Neumann boundary condition. Electronic journal of differential equations [na spletu]. 2018. Vol. 2018, p. art. no. 41,  1-10. [Dostopano 21 april 2025]. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=109446

Gradivo je del revije

• Naslov: Electronic journal of differential equations
• Skrajšan naslov: Electr. j. differ. equ.
• Založnik: Southwest Texas State University, University of North Texas
• ISSN: 1072-6691
• COBISS.SI-ID: 7027289