Three solutions for a nonlocal problem with critical growth
نویسندگان
چکیده
منابع مشابه
Existence of Solutions to a Nonlocal Boundary Value Problem with Nonlinear Growth
Copyright q 2011 Xiaojie Lin. 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. This paper deals with the existence of solutions for the following differential equation: x′′ t f t, x t , x′ t , t ∈ 0, 1 , subject to the boundary con...
متن کاملPositive Solutions to a Linearly Perturbed Critical Growth Biharmonic Problem
Existence and nonexistence results for positive solutions to a linearly perturbed critical growth biharmonic problem under Steklov boundary conditions, are determined. Furthermore, by investigating the critical dimensions for this problem, a Sobolev inequality with remainder terms, of both interior and boundary type, is deduced.
متن کاملRemarks on weak solutions for a nonlocal parabolic problem
where Ω is a smooth bounded open subset of RN with regular boundary Γ. In problem (1.1) a and f are both continuous functions, whose properties will be introduced when necessary, l : L2(Ω) → R is a nonlinear form, h ∈ L2(0,T ;H−1(Ω)), and T > 0 is some fixed time. System (1.1) is studied, for instance, in papers of Chipot and Lovat [4] in case f = f (x) depends only on the variable x. In this w...
متن کاملPositive solutions for a nonlinear nonlocal elliptic transmission problem
K e y w o r d s E l l i p t i c system, Transmission problem, Positive solution. 1. I N T R O D U C T I O N Let 12 be a smooth bounded domain of R n, n > 2, and let ~1 c gl be a subdomain with smooth boundary ~ satisfying ~1 C i2. Writing F = c9~ and gl2 = ~\~l l we have ~ = ~1 tJ 122 and 0i'~2 = ~, tJ F. We are concerned with the existence of positive solutions to the following system of nonli...
متن کاملExploding solutions for a nonlocal quadratic evolution problem
We consider a nonlinear parabolic equation with fractional diffusion which arises from modelling chemotaxis in bacteria. We prove the wellposedness, continuation criteria and smoothness of local solutions. In the repulsive case we prove global wellposedness in Sobolev spaces. Finally in the attractive case, we prove that for a class of smooth initial data the L∞x -norm of the corresponding solu...
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 Mathematical Analysis and Applications
سال: 2019
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2018.09.038