Liouville-type theorems for the fourth order nonlinear elliptic equation
نویسندگان
چکیده
منابع مشابه
A Fourth Order Elliptic Equation with Nonlinear Boundary Conditions
In this paper we study the existence of infinitely many nontrivial solutions of the following problem, −∆2u = u in Ω, − ∂∆u ∂ν = f(x, u) on ∂Ω, and either ∂u ∂ν = 0 or ∆u = 0 on ∂Ω. We assume that f(x, u) is superlinear and either subcritical or a sublinear perturbation of the critical case. For the proof in the critical case we apply the concentration compactness method.
متن کاملA Fourth Order Nonlinear Elliptic Equation with Jumping Nonlinearity
We investigate the existence of solutions of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition A2u + CAU = bu+ + f in 0, where R is a bounded open set in Rn with smooth boundary and the nonlinearity bu+ crosses eigenvalues of A2 + CA. We also investigate a relation between multiplicity of solutions and source terms of the equation with the nonlinearit...
متن کاملLiouville-type theorems for stable and finite Morse index solutions of a quasi-linear elliptic equation
We establish Liouville-type theorems for stable and finite Morse index weak solutions of −∆pu = f(x)F (u) in R . For a general non-linearity F ∈ C(R) and f(x) = |x|, we prove such theorems in dimensions N ≤ 4(p+α) p−1 +p, for bounded radial stable solutions. Then, we give some point-wise estimates for not necessarily bounded solutions. Also, similar theorems will be proved for both radial finit...
متن کاملLiouville-type theorems for fully nonlinear elliptic equations and systems in half spaces
In [LWZ], we established Liouville-type theorems and decay estimates for solutions of a class of high order elliptic equations and systems without the boundedness assumptions on the solutions. In this paper, we continue our work in [LWZ] to investigate the role of boundedness assumption in proving Liouville-type theorems for fully nonlinear equations. We remove the boundedness assumption of sol...
متن کاملLiouville-type theorems and decay estimates for solutions to higher order elliptic equations
Liouville-type theorems are powerful tools in partial differential equations. Boundedness assumption of solutions are often imposed in deriving such Liouville-type theorems. In this paper, we establish some Liouville-type theorems without the boundedness assumption of nonnegative solutions to certain classes of elliptic equations and systems. Using a rescaling technique and doubling lemma devel...
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: Journal of Differential Equations
سال: 2014
ISSN: 0022-0396
DOI: 10.1016/j.jde.2013.12.001