Radially Symmetric Solutions of a Nonlinear Elliptic Equation
نویسندگان
چکیده
منابع مشابه
Radially Symmetric Solutions of a Nonlinear Elliptic Equation
We investigate the existence and asymptotic behavior of positive, radially symmetric singular solutions of w′′ N − 1 /r w′ − |w|p−1w 0, r > 0. We focus on the parameter regime N > 2 and 1 < p < N/ N − 2 where the equation has the closed form, positive singular solution w1 4 − 2 N − 2 p − 1 / p − 1 2 1/ p−1 r−2/ p−1 , r > 0. Our advance is to develop a technique to efficiently classify the behav...
متن کاملNumerical Approximation of Blow-Up of Radially Symmetric Solutions of the Nonlinear Schrödinger Equation
We consider the initial-value problem for the radially symmetric nonlinear Schrödinger equation with cubic nonlinearity (NLS) in d = 2 and 3 space dimensions. To approximate smooth solutions of this problem, we construct and analyze a numerical method based on a standard Galerkin finite element spatial discretization with piecewise linear, continuous functions and on an implicit Crank–Nicolson ...
متن کاملRadially symmetric nonlinear photonic crystals
Different types of quadratic, radially symmetric, nonlinear photonic crystals are presented. The modulation of the nonlinear coefficient may be a periodic or an aperiodic function of the radial coordinate, whereas the azimuthal symmetry of the crystal may be either continuous or discrete. Nonlinear interactions within these structures are studied in two orientations, transverse and longitudinal...
متن کاملRadially Symmetric Solutions for a Class ofCritical Exponent Elliptic Problems in RN
We give a method for obtaining radially symmetric solutions for the critical exponent problem ?u + a(x)u = u q + u 2 ?1 in R N u > 0 and R R N jruj 2 < 1 where, outside a ball centered at the origin, the non-negative function a is bounded from below by a positive constant ao > 0. We remark that, diierently from the literature, we do not require any conditions on a at innnity.
متن کاملRadially-symmetric Problems of Nonlinear Viscoelasticity
Title of dissertation: ANALYSIS OF STEADY-STATE AND DYNAMICAL RADIALLY-SYMMETRIC PROBLEMS OF NONLINEAR VISCOELASTICITY Alexey B. Stepanov, Doctor of Philosophy, 2015 Dissertation directed by: Professor Stuart S. Antman Department of Mathematics This thesis treats radially symmetric steady states and radially symmetric motions of nonlinearly elastic and viscoelastic plates and shells subject to ...
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: International Journal of Mathematics and Mathematical Sciences
سال: 2011
ISSN: 0161-1712,1687-0425
DOI: 10.1155/2011/608576