Fractional Kirchhoff equation with a general critical nonlinearity
نویسندگان
چکیده
منابع مشابه
Ground States for Fractional Kirchhoff Equations with Critical Nonlinearity in Low Dimension
We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential V . Under suitable assumptions on V , using the monotonicity trick and the profile decomposition, we prove the existence of ground states. In particular, the nonlinearity does not satisfy the Ambrosetti-Rabinowitz type condition or monotonicity assumptions.
متن کاملDamped Wave Equation with a Critical Nonlinearity
We study large time asymptotics of small solutions to the Cauchy problem for nonlinear damped wave equations with a critical nonlinearity { ∂2 t u+ ∂tu−∆u+ λu 2 n = 0, x ∈ Rn, t > 0, u(0, x) = εu0 (x) , ∂tu(0, x) = εu1 (x) , x ∈ Rn, where ε > 0, and space dimensions n = 1, 2, 3. Assume that the initial data u0 ∈ H ∩H, u1 ∈ Hδ−1,0 ∩H−1,δ, where δ > n 2 , weighted Sobolev spaces are H = { φ ∈ L; ...
متن کاملA Diffusion Equation with Exponential Nonlinearity Recant Developments
The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...
متن کاملOn a geometric equation with critical nonlinearity on the boundary
A theorem of Escobar asserts that, on a positive three dimensional smooth compact Riemannian manifold with boundary which is not conformally equivalent to the standard three dimensional ball, a necessary and sufficient condition for a C2 function H to be the mean curvature of some conformal scalar flat metric is that H is positive somewhere. We show that, when the boundary is umbilic and the fu...
متن کاملExistence and Uniform Decay for a Nonlinear Beam Equation with Nonlinearity of Kirchhoff Type in Domains with Moving Boundary
We prove the exponential decay in the case n > 2, as time goes to infinity, of regular solutions for the nonlinear beam equation with memory and weak damping utt + ∆2u− M(‖∇u‖L2(Ωt))∆u + ∫ t 0 g(t − s)∆u(s)ds + αut = 0 in ∧ Q in a noncylindrical domain of Rn+1 (n ≥ 1) under suitable hypothesis on the scalar functions M and g, and where α is a positive constant. We establish existence and unique...
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: Applied Mathematics Letters
سال: 2017
ISSN: 0893-9659
DOI: 10.1016/j.aml.2017.06.003