相关论文: Lie Symmetries and Criticality of Semilinear Diffe…
We show that all Lie point symmetries of various classes of nonlinear differential equations involving critical nonlinearities are variational/divergence symmetries.
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
Lie symmetry analysis is an established method for generating symmetries of differential equations. We apply this method together the generalized fundamental theorem of double reduction. In particular, Noether symmetries and some associated…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
Several nonlinear stochastic differential equations have been proposed in connection with self-organized critical phenomena. Due to the threshold condition involved in its dynamic evolution an infinite number of nonlinearities arises in a…
We demonstrate the fact that linearity is a meaningful symmetry in the sense of Lie and Noether. The role played by that `linearity symmetry' in the quadrature of linear ordinary second-order differential equations is reviewed, by the use…
The Lie symmetry analysis for the study of a $1+n~$fourth-order Schr\"{o}dinger equation inspired by the modification of the deformation algebra in the presence of a minimum length is applied. Specifically, we perform a detailed…
Quantum phase transitions are a fascinating area of condensed matter physics. The extension through complexification not only broadens the scope of this field but also offers a new framework for understanding criticality and its statistical…
We establish the existence and nonexistence of entire solutions to a semilinear elliptic problem whose nonlinearity is the critical power multiplied by a function that takes the value 1 in an open bounded region and the value -1 in its…
Two essential methods, the symmetry analysis and of the singularity analysis, for the study of the integrability of nonlinear ordinary differential equations are discussed. The main similarities and differences of these two different…
We show that any Lie point symmetry of semilinear Kohn-Laplace equations on the Heisenberg group H^1 with power nonlinearity is a divergence symmetry if and only if the corresponding exponent assumes critical value.
Symmetry breaking plays a pivotal role in modern physics. Although self-similarity is also a symmetry and appears ubiquitously in nature, a fundamental question is whether self-similarity breaking makes sense or not. Here, by identifying…
Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are…
A {\it Lie system} is a nonautonomous system of first-order differential equations admitting a {\it superposition rule}, i.e., a map expressing its general solution in terms of a generic family of particular solutions and some constants.…
In this paper, by utilizing a newly established variational principle on convex sets, we provide an existence and multiplicity result for a class of semilinear elliptic problems defined on the whole $\mathbb R^N$ with nonlinearities…
We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a…
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…
We investigate qualitative properties of positive singular solutions of some elliptic systems in bounded and unbounded domains. We deduce symmetry and monotonicity properties via the moving plane procedure. Moreover, in the unbounded case,…
The main thrust of our current work is to exploit very specific characteristics of a given problem in order to acquire improved compactness for supercritical problems and to prove existence of new types of solutions. To this end, we shall…
It was proved in [14] that the existence of a noncritical multiplier for a (smooth) nonlinear programming problem is equivalent to an error bound condition for the Karush-Kuhn-Thcker (KKT) system without any assumptions. This paper…