Existence result for a nonlinear elliptic problem by topological degree in Sobolev spaces with variable exponent
نویسندگان
چکیده
منابع مشابه
Nonlinear eigenvalue problems in Sobolev spaces with variable exponent
Abstract. We study the boundary value problem −div((|∇u|1 + |∇u|2)∇u) = f(x, u) in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in R . We focus on the cases when f±(x, u) = ±(−λ|u| u+ |u|u), where m(x) := max{p1(x), p2(x)} < q(x) < N ·m(x) N−m(x) for any x ∈ Ω. In the first case we show the existence of infinitely many weak solutions for any λ > 0. In the second case we prove that if λ is...
متن کاملAn existence result for nonlinear elliptic problems involving critical Sobolev exponent
In this paper we consider the following problem: where Q c Rn is a bounded domain and We prove the existence of a nontrivial solution of (1) for any ~, > 0, RESUME. Soient Q un sous-ensemble ouvert borne de Rn et À un nombre positif, le but de cette note c’est de montrer que le probleme suivant : admet, au moins, une solution non triviale, si r~ > 4. Work supported by G. N. A. F. A. o...
متن کاملOn a nonlinear eigenvalue problem in Sobolev spaces with variable exponent
Abstract. We consider a class of nonlinear Dirichlet problems involving the p(x)–Laplace operator. Our framework is based on the theory of Sobolev spaces with variable exponent and we establish the existence of a weak solution in such a space. The proof relies on the Mountain Pass Theorem.
متن کاملExistence of solutions for elliptic systems with critical Sobolev exponent ∗
We establish conditions for existence and for nonexistence of nontrivial solutions to an elliptic system of partial differential equations. This system is of gradient type and has a nonlinearity with critical growth.
متن کاملExistence of Multiple Solutions for a Singular Elliptic Problem with Critical Sobolev Exponent
and Applied Analysis 3 The following Hardy-Sobolev inequality is due to Caffarelli et al. 12 , which is called Caffarelli-Kohn-Nirenberg inequality. There exist constants S1, S2 > 0 such that (∫ RN |x|−bp |u|pdx )p/p∗ ≤ S1 ∫ RN |x|−ap|∇u|pdx, ∀u ∈ C∞ 0 ( R N ) , 1.8 ∫ RN |x|− a 1 |u|dx ≤ S2 ∫ RN |x|−ap|∇u|pdx, ∀u ∈ C∞ 0 ( R N ) , 1.9 where p∗ Np/ N − pd is called the Sobolev critical exponent. ...
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: Moroccan Journal of Pure and Applied Analysis
سال: 2020
ISSN: 2351-8227
DOI: 10.2478/mjpaa-2021-0006