Nonlinear biharmonic equations with negative exponents
نویسندگان
چکیده
منابع مشابه
Liouville Type Results and Regularity of the Extremal Solutions of Biharmonic Equation with Negative Exponents
We first obtain Liouville type results for stable entire solutions of the biharmonic equation −∆2u = u−p in R for p > 1 and 3 ≤ N ≤ 12. Then we consider the Navier boundary value problem for the corresponding equation and improve the known results on the regularity of the extremal solution for 3 ≤ N ≤ 12. As a consequence, in the case of p = 2, we show that the extremal solution u∗ is regular w...
متن کاملRegularity of the Solutions for Nonlinear Biharmonic Equations in R
The purpose of this paper is to establish the regularity the weak solutions for the nonlinear biharmonic equation { ∆2u + a(x)u = g(x, u), u ∈ H2(RN ), where the condition u ∈ H2(RN ) plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense.
متن کاملOn Two Nonlinear Biharmonic Evolution Equations: Existence, Uniqueness and Stability
We study the following two nonlinear evolution equations with a fourth order (biharmonic) leading term: −∆2u− 1 22 (|u|2 − 1)u = ut in Ω ⊂ R or R and −∆2u + 1 22 ∇ · ((|∇u|2 − 1)∇u) = ut in Ω ⊂ R or R with an initial value and a Dirichlet boundary conditions. We show the existence and uniqueness of the weak solutions of these two equations. For any t ∈ [0,+∞), we prove that both solutions are i...
متن کاملNumerical Simulations on Two Nonlinear Biharmonic Evolution Equations
We numerically simulate the following two nonlinear evolution equations with a fourth order (biharmonic) leading term: −∆2u− 1 22 (|u|2 − 1)u = ut in Ω ⊂ R or R and −∆2u + 1 22 ∇ · ((|∇u|2 − 1)∇u) = ut in Ω ⊂ R or R with an initial value and a Dirichlet boundary conditions. We use a bivariate spline space like finite element method to solve these equations. We discuss the convergence of our num...
متن کاملSupercritical biharmonic equations with power-type nonlinearity
The biharmonic supercritical equation ∆u = |u|p−1u, where n > 4 and p > (n + 4)/(n − 4), is studied in the whole space R as well as in a modified form with λ(1 + u) as right-hand-side with an additional eigenvalue parameter λ > 0 in the unit ball, in the latter case together with Dirichlet boundary conditions. As for entire regular radial solutions we prove oscillatory behaviour around the expl...
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: 2009
ISSN: 0022-0396
DOI: 10.1016/j.jde.2008.06.027