Large versus bounded solutions to sublinear elliptic problems
نویسندگان
چکیده
منابع مشابه
Existence of Positive Bounded Solutions of Semilinear Elliptic Problems
Correspondence should be addressed to Faten Toumi, [email protected] Received 18 June 2010; Accepted 25 September 2010 Academic Editor: A. Mikelic Copyright q 2010 Faten Toumi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Thi...
متن کاملExact multiplicity of solutions to superlinear and sublinear problems
(f2) lim u→∞ f(u) u =f+ ¿ 0; lim u→−∞ f(u) u =f− ¿ 0: For the de5niteness, we assume f+ ¿f−, and when f+ =f−, we use f± to represent it. We will consider f being either superlinear or sublinear. f is said to be superlinear if f(u)=u is decreasing in (0;∞) and is increasing in (−∞; 0); and f is said to be sublinear if f(u)=u is increasing in (0;∞) and is decreasing in (−∞; 0): The semilinear equ...
متن کاملEntire solutions of sublinear elliptic equations in anisotropic media
We study the nonlinear elliptic problem −∆u = ρ(x)f(u) in R (N ≥ 3), lim|x|→∞ u(x) = l, where l ≥ 0 is a real number, ρ(x) is a nonnegative potential belonging to a certain Kato class, and f(u) has a sublinear growth. We distinguish the cases l > 0 and l = 0 and we prove existence and uniqueness results if the potential ρ(x) decays fast enough at infinity. Our arguments rely on comparison techn...
متن کاملA Priori Estimates of Positive Solutions for Sublinear Elliptic Equations
In this paper, a priori estimates of positive solutions for sublinear elliptic equations are given in terms of thicknesses of domains. To this end, a supersolution is constructed by a composite function of a solution to an ordinary differential equation and a distance function. The results work efficiently in the case where the domain is an exterior or an interior of a convex set.
متن کاملCharacterizing the existence of large solutions for a class of sublinear problems with nonlinear diffusion
In this paper we characterize the existence of large solutions for a general class of sublinear elliptic problems of logistic type related to the porous media equation. Our main result shows that large solutions do exist if, and only if, the nonlinear diffusion is not too large. As a byproduct of the general theory developed by the authors in [2], those large solutions must be unstable with res...
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: Bulletin of the Polish Academy of Sciences Mathematics
سال: 2019
ISSN: 0239-7269,1732-8985
DOI: 10.4064/ba8180-12-2018