Energy functionals of Kirchhoff-type problems having multiple global minima
نویسندگان
چکیده
منابع مشابه
Integral functionals on Sobolev spaces having multiple local minima
THEOREM A. Let (X, τ) be a Hausdorff topological space and Ψ : X →]−∞,+∞], Φ : X → R two functions. Assume that there is r > infX Ψ such that the set Ψ (]−∞, r]) is compact and first-countable. Moreover, suppose that the function Φ is bounded below in Ψ(]−∞, r]) and that the function Ψ+ λΦ is sequentially lower semicontinuous for each λ ≥ 0 small enough. Finally, assume that the set of all glob...
متن کاملMultiple Sign-changing Solutions for Kirchhoff Type Problems
This article concerns the existence of sign-changing solutions to nonlocal Kirchhoff type problems of the form
متن کاملMinima of Non Coercive Functionals
In this paper we study a class of integral functionals defined on H 0 (Ω), but non coercive on the same space, so that the standard approach of the Calculus of Variations does not work. However, the functionals are coercive on W 1,1 0 (Ω) and we will prove the existence of minima, despite the non reflexivity of W 1,1 0 (Ω), which implies that, in general, the Direct Methods fail due to lack of ...
متن کاملGlobal minima for semilinear optimal control problems
We consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization. We provide a condition which allows to decide whether a solution of the necessary first order conditions is a global minimum. This condition can be explicitly evaluated at the discrete level. Furthermore, we prove that if the above condition holds uniformly with respect to t...
متن کاملNontrivial solutions of Kirchhoff type problems
In this paper, we study Kirchhoff type problems on a bounded domain. We consider the cases that the nonlinearity is superlinear near zero but asymptotically 4-linear at infinity, and the nonlinearity is asymptotically linear near zero but 4-superlinear at infinity. By computing the relevant critical groups, we obtain nontrivial solutions via Morse theory.
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: 2015
ISSN: 0362-546X
DOI: 10.1016/j.na.2014.12.012