منابع مشابه
On an elliptic Kirchhoff-type problem depending on two parameters
Let Ω ⊂ R be a bounded domain with smooth boundary, and let K : [0,+∞[→ R be a given continuous function. If n ≥ 2, we denote by A the class of all Carathéodory functions φ : Ω×R → R such that sup (x,t)∈Ω×R |φ(x, t)| 1 + |t|q < +∞ , where 0 < q < n+2 n−2 if n > 2 and 0 < q < +∞ if n = 2. While, when n = 1, we denote by A the class of all Carathéodory functions φ : Ω ×R → R such that, for each r...
متن کاملOn a Perturbed Dirichlet Problem for a Nonlocal Differential Equation of Kirchhoff Type
We study the existence of positive solutions to the following nonlocal boundary value problem −K ‖u‖2 Δu λus−1 f x, u inΩ, u 0 on ∂Ω, where s ∈ 1, 2 , f : Ω×R → R is a Carathéodory function,K : R → R is a positive continuous function, and λ is a real parameter. Direct variational methods are used. In particular, the proof of the main result is based on a property of the infimum on certain spher...
متن کامل2 00 9 On an elliptic Kirchhoff - type problem depending on two parameters BIAGIO RICCERI
Let Ω ⊂ R be a bounded domain with smooth boundary, and let K : [0,+∞[→ R be a given continuous function. If n ≥ 2, we denote by A the class of all Carathéodory functions φ : Ω×R → R such that sup (x,t)∈Ω×R |φ(x, t)| 1 + |t|q < +∞ , where 0 < q < n+2 n−2 if n > 2 and 0 < q < +∞ if n = 2. While, when n = 1, we denote by A the class of all Carathéodory functions φ : Ω ×R → R such that, for each r...
متن کاملOn a class of Kirchhoff type systems with nonlinear boundary condition
A class of Kirchhoff type systems with nonlinear boundary conditions considered in this paper. By using the method of Nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.
متن کاملSolutions of a Nonlocal Elliptic Problem Involving p(x)-Kirchhoff-type Equation
The present paper deals with a Kirchhoff problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain Ω of R^{N}. The problem studied is a stationary version of the orig inal Kirchhoff equation, involving the p(x)-Lap lacian operator, in the framework of the variable exponent Lebesgue and Sobolev spaces. The question of the existence of weak solutions is treated. Appl...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2015
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2014.12.017