Existence of Positive Weak Solutions for Fractional Lane–emden Equations with Prescribed Singular Sets
نویسندگان
چکیده
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 weak solutions with S as its singular set. We also show the existence of solutions to the fractional Yamabe problem with singular set to be the whole space Rn. These results are the extension of Chen and Lin’s result [9] to the fractional case.
منابع مشابه
New 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 کاملInterval fractional integrodifferential equations without singular kernel by fixed point in partially ordered sets
This work is devoted to the study of global solution for initial value problem of interval fractional integrodifferential equations involving Caputo-Fabrizio fractional derivative without singular kernel admitting only the existence of a lower solution or an upper solution. Our method is based on fixed point in partially ordered sets. In this study, we guaranty the existence of special kind of ...
متن کاملMODIFICATION OF THE OPTIMAL HOMOTOPY ASYMPTOTIC METHOD FOR LANE-EMDEN TYPE EQUATIONS
In this paper, modication of the optimal homotopy asymptotic method (MOHAM) is appliedupon singular initial value Lane-Emden type equations and results are compared with the available exactsolutions. The modied algorithm give the exact solution for dierential equations by using one iterationonly.
متن کاملA Third-degree B-spline Collocation Scheme for Solving a Class of the Nonlinear Lane–-Emden Type Equations
In this paper, we use a numerical method involving collocation method with third B-splines as basis functions for solving a class of singular initial value problems (IVPs) of Lane--Emden type equation. The original differential equation is modified at the point of singularity. The modified problem is then treated by using B-spline approximation. In the case of non-linear problems, we first line...
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 کامل