Semilinear Elliptic Equations on Thin Network-Shaped Domains with Variable Thickness
نویسندگان
چکیده
منابع مشابه
Semilinear Elliptic Equations in Thin Domains with Reaction Terms Concentrating on Boundary
In this paper we analyze the behavior of a family of steady state solutions of a semilinear reaction-diffusion equation with homogeneous Neumann boundary condition, posed in a two-dimensional thin domain whit reaction terms concentrated in a narrow oscillating neighborhood of the boundary. We assume that the domain, and therefore, the oscillating boundary neighborhood, degenerates into an inter...
متن کاملPalais-smale Approaches to Semilinear Elliptic Equations in Unbounded Domains
Let Ω be a domain in RN , N ≥ 1, and 2∗ = ∞ if N = 1, 2, 2∗ = 2N N−2 if N > 2, 2 < p < 2 ∗. Consider the semilinear elliptic problem −∆u+ u = |u|p−2u in Ω; u ∈ H 0 (Ω). Let H1 0 (Ω) be the Sobolev space in Ω. The existence, the nonexistence, and the multiplicity of positive solutions are affected by the geometry and the topology of the domain Ω. The existence, the nonexistence, and the multipli...
متن کاملLiouville type results for semilinear elliptic equations in unbounded domains
This paper is devoted to the study of some class of semilinear elliptic equations in the whole space: −aij(x)∂iju(x)− qi(x)∂iu(x) = f(x, u(x)), x ∈ R . The aim is to prove uniqueness of positive bounded solutions Liouville type theorems. Along the way, we establish also various existence results. We first derive a sufficient condition, directly expressed in terms of the coefficients of the line...
متن کاملPositive solutions to singular semilinear elliptic equations with critical potential on cone–like domains
We study the existence and nonexistence of positive (super-) solutions to a singular semilinear elliptic equation −∇ · (|x|∇u)−B|x|u = C|x|u in cone–like domains of R (N ≥ 2), for the full range of parameters A,B, σ, p ∈ R and C > 0. We provide a complete characterization of the set of (p, σ) ∈ R such that the equation has no positive (super-) solutions, depending on the values of A,B and the p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2002
ISSN: 0022-0396
DOI: 10.1006/jdeq.2001.4119