A note on a second order PDE with critical nonlinearity
نویسندگان
چکیده
منابع مشابه
A Note on a Fourth Order Pde with Critical Nonlinearity
(1.3) 2(1 + α)∆w + 2β div ( αD(|Dw|2)− (α∆w + β|Dw|2)Dw) = div(T (Dw, ·))− (E′(w − w)− E′(w − w)) where E′(w − w) = 1 volM ∫ E′(w − w). Chang, Gursky and Yang [CGY] proved that any F -minimizing solution u ∈ W 2,2(M) to (1.3) is actually smooth. It was asked in [CGY] whether any weak solution u ∈ W 2,2(M) is smooth. Indeed, Uhlenbeck and Viaclovsky [UV] confirmed this recently and proved the sm...
متن کاملA RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION
Let U(t, ) be solution of the Dirichlet problem y''+( t-q(t))y= 0 - 1 t l y(-l)= 0 = y(x), with variabIe t on (-1, x), for fixed x, which satisfies the initial condition U(-1, )=0 , (-1, )=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigen values has been investigated . Furthermore, the leading term of the asymptotic formula for ...
متن کاملHarmonic entanglement with second-order nonlinearity.
We investigate the second-order nonlinear interaction as a means to generate entanglement between fields of differing wavelengths and show that perfect entanglement can, in principle, be produced between the fundamental and second-harmonic fields in these processes. Neither pure second-harmonic generation nor parametric oscillation optimally produce entanglement; such optimal entanglement is ra...
متن کاملBang-bang control of a second-order non-linear stable plant with second-order nonlinearity
In this paper the design of a controller for a relay-controlled second-order non-linear stable plant with second-order nonlinearity is considered. The task of the controller is the simultaneous reduction of plant's output and output derivative to zero with the input to the feedback system being at z;ro. It will be shown that for all initial values ot output and output derivative it would be pos...
متن کاملA note on the order graph of a group
The order graph of a group $G$, denoted by $Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|big{|}|K|$ or $|K|big{|}|H|$. In this paper, we study the connectivity and diameter of this graph. Also we give a relation between the order graph and prime graph of a group.
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: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2019
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2019.1.10