On Finite Morse Index Solutions of Higher Order Fractional Lane-emden Equations
نویسندگان
چکیده
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 and Wei in [7].
منابع مشابه
On the Fractional Lane-emden Equation
We classify solutions of finite Morse index of the fractional LaneEmden equation (−∆)su = |u|p−1u in R.
متن کاملNew Solutions for Singular Lane-Emden Equations Arising in Astrophysics Based on Shifted Ultraspherical Operational Matrices of Derivatives
In this paper, the ultraspherical operational matrices of derivatives are constructed. Based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems. The basic idea behind the suggested algorithms is basically built on transforming the eq...
متن کاملSolving nonlinear Lane-Emden type equations with unsupervised combined artificial neural networks
In this paper we propose a method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-innite domain. The proposed approach is based on an Unsupervised Combined Articial Neural Networks (UCANN) method. Firstly, The trial solutions of the differential equations are written in the form of feed-forward neural networks cont...
متن کاملOn the Hénon-Lane-Emden conjecture
We consider the problem of non-existence of solutions for the following Hénon-Lane-Emden system −∆u = |x|v in R , −∆v = |x|u in R , when pq > 1, p, q, a, b ≥ 0, and (p, q) are under the critical hyperbola, i.e. N+a p+1 + N+b q+1 > N − 2. We show that there is no positive bounded solution in dimension N = 3, extending a result established recently by Phan-Souplet in the scalar case. This solve...
متن کاملNumerical Study of Fractional Differential Equations of Lane-Emden Type by Method of Collocation
Lane-Emden differential equations of order fractional has been studied. Numerical solution of this type is considered by collocation method. Some of examples are illustrated. The comparison between numerical and analytic methods has been introduced.
متن کامل