On finite Morse index solutions of higher order fractional Lane-Emden equations
نویسندگان
چکیده
منابع مشابه
On Finite Morse Index Solutions of Higher Order Fractional Lane-emden Equations
We classify finite Morse index solutions of the following nonlocal Lane-Emden equation (−∆)u = |u|p−1u R for 1 < s < 2 via a novel monotonicity formula. For local cases s = 1 and s = 2 this classification is provided by Farina in [10] and Davila, Dupaigne, Wang and Wei in [8], respectively. Moreover, for the nonlocal case 0 < s < 1 finite Morse index solutions are classified by Davila, Dupaigne...
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 کاملOn 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 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: American Journal of Mathematics
سال: 2017
ISSN: 1080-6377
DOI: 10.1353/ajm.2017.0011