On positive viscosity solutions of fractional Lane-Emden systems
نویسندگان
چکیده
منابع مشابه
On Stable Solutions of the Fractional Henon-lane-emden Equation
We derive a monotonicity formula for solutions of the fractional Hénon-Lane-Emden equation (−∆)u = |x|a|u|p−1u R where 0 < s < 2, a > 0 and p > 1. Then we apply this formula to classify stable solutions of the above equation.
متن کاملOn the Fractional Lane-emden Equation
We classify solutions of finite Morse index of the fractional LaneEmden equation (−∆)su = |u|p−1u in R.
متن کاملExistence of Positive Weak Solutions for Fractional Lane–emden Equations with Prescribed Singular Sets
In this paper, we consider the problem of the existence of positive weak solutions of { (−∆)su = up in Ω u = 0 on Rn\Ω having prescribed isolated interior singularities. We prove that if n n−2s < p < p1 for some critical exponent p1 defined in the introduction which is related to the stability of the singular solution us, and if S is a closed subset of Ω, then there are infinitely many positive...
متن کاملOn Lane-emden Type Systems
We consider a class of singular systems of Lane-Emden type ∆u + λu p 1 v q 1 = 0, x ∈ D, a smooth domain in R n. In case the system is sublinear we prove existence of a positive solution. If D is a ball in R n , we prove both existence and uniqueness of positive radially symmetric solution.
متن کاملSeparable solutions of quasilinear Lane-Emden equations
For 0 < p − 1 < q and either ǫ = 1 or ǫ = −1, we prove the existence of solutions of −∆pu = ǫu q in a cone CS , with vertex 0 and opening S, vanishing on ∂CS , under the form u(x) = |x|ω( x |x|). The problem reduces to a quasilinear elliptic equation on S and existence is based upon degree theory and homotopy methods. We also obtain a non-existence result in some critical case by an integral ty...
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: Topological Methods in Nonlinear Analysis
سال: 2019
ISSN: 1230-3429
DOI: 10.12775/tmna.2019.005