Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities

Conformally invariant fully nonlinear elliptic equations and isolated singularities

1 Introduction There has been much work on conformally invariant fully nonlinear elliptic equations and applications to geometry and topology. [10], and the references therein. In this and a companion paper [16] we address some analytical issues concerning these equations. For n ≥ 3, consider −∆u = n − 2 2 u n+2 n−2 , on R n .

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Oscillation and Asymptotic Behavior of Higher-Order Nonlinear Differential Equations

Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations

We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very close to a single standard bubble in a universal positive distance around each blow-up point, and (i...

On qualitative properties and asymptotic behavior of solutions to higher-order nonlinear differential equations

We discuss the asymptotic behavior of solutions to a higher-order Emden–Fowler type equation with constant potential. Several author’s results are presented concerning both positive and oscillatory solutions to equations with regular and singular nonlinearities. We discuss the existence and asymptotic behavior of “blowup” solutions. Results on the asymptotic behavior of oscillating solutions ar...