Oddness of least energy nodal solutions on radial domains.
On a Parabolic Symmetry Problem.
On a priori estimates for positive solutions of a semilinear biharmonic equation in a ball
On a quasilinear elliptic equation and a Riemannian metric invariant under Möbius transformations.
On a quasilinear elliptic equation and a Riemannian metric invariant under Möbius transformations. (Summary).
On decomposable Monge-Ampère equations.
On formal theory of differential equations. I.
On formal theory of differential equations. II.
On formal theory of differential equations. III.
Elements of the general theory of Lie-Cartan pseudogroups (including the intransitive case) are developed within the framework of infinitely prolonged systems of partial differential equations (diffieties) which makes it independent of any particular realizations by transformations of geometric object. Three axiomatic approaches, the concepts of essential invariant, subgroup, normal subgroup and factorgroups are discussed. The existence of a very special canonical composition series based on Cauchy...
On functions, whose lines of steepest descent bend proportionally to level lines
On linearizing systems of diffusion equations.
On the continuation of solutions for elliptic equations in two variables
On the Dirac delta as initial condition for nonlinear Schrödinger equations
On the generalized Maxwell-Bloch equations.
On the mixed problem for hyperbolic partial differential-functional equations of the first order
We consider the mixed problem for the hyperbolic partial differential-functional equation of the first order where is a function defined by , . Using the method of bicharacteristics and the method of successive approximations for a certain integral-functional system we prove, under suitable assumptions, a theorem of the local existence of generalized solutions of this problem.
On the nodal set of the second eigenfunction of the laplacian in symmetric domains in
We present a simple proof of the fact that if is a bounded domain in , , which is convex and symmetric with respect to orthogonal directions, , then the nodal sets of the eigenfunctions of the laplacian corresponding to the eigenvalues must intersect the boundary. This result was proved by Payne in the case for the second eigenfunction, and by other authors in the case of convex domains in the plane, again for the second eigenfunction.
On the static and dynamic study of oscillations for some nonlinear hyperbolic systems of conservation laws
On the symmetries of the differential equation governing damped harmonic vibration.
On the symmetry of blowup solutions to a mean field equation
On the uniqueness of the Cauchy problem for partial differential operators with multiple characteristics