Entire solutions of multivalued nonlinear Schrödinger equations in Sobolev spaces with variable exponent
نویسندگان
چکیده
منابع مشابه
Entire solutions of multivalued nonlinear Schrodinger equations in Sobolev spaces with variable exponent
We establish the existence of an entire solution for a class of stationary Schrödinger equations with subcritical discontinuous nonlinearity and lower bounded potential that blows-up at infinity. The abstract framework is related to Lebesgue–Sobolev spaces with variable exponent. The proof is based on the critical point theory in the sense of Clarke and we apply Chang’s version of the Mountain ...
متن کاملNonlinear 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 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 کاملVector-valued Inequalities on Herz Spaces and Characterizations of Herz–sobolev Spaces with Variable Exponent
The origin of Herz spaces is the study of characterization of functions and multipliers on the classical Hardy spaces ([1, 8]). By virtue of many authors’ works Herz spaces have became one of the remarkable classes of function spaces in harmonic analysis now. One of the important problems on the spaces is boundedness of sublinear operators satisfying proper conditions. Hernández, Li, Lu and Yan...
متن کاملEntire solutions of nonlinear differential-difference equations
In this paper, we describe the properties of entire solutions of a nonlinear differential-difference equation and a Fermat type equation, and improve several previous theorems greatly. In addition, we also deduce a uniqueness result for an entire function f(z) that shares a set with its shift [Formula: see text], which is a generalization of a result of Liu.
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: Nonlinear Analysis: Theory, Methods & Applications
سال: 2006
ISSN: 0362-546X
DOI: 10.1016/j.na.2005.10.022