Comparison theorems for elliptic equations on unbounded domains
نویسندگان
چکیده
منابع مشابه
Liouville 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 کاملAttractors for Modulation Equations on Unbounded Domains { Existence and Comparison {
We are interested in the long{time behavior of nonlinear parabolic PDEs deened on unbounded cylindrical domains. For dissipative systems deened on bounded domains, the long{time behavior can often be described by the dynamics in their nite{dimensional attractors. For systems deened on the innnite line, very little is known at present, since the lack of compactness prevents application of the st...
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 کاملPullback D-attractors for non-autonomous partly dissipative reaction-diffusion equations in unbounded domains
At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.
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: Transactions of the American Mathematical Society
سال: 1967
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1967-0203211-9