Observations on quasi-linear partial differential equations
On a fourth order equation in 3-D
In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.
On a Fourth Order Equation in 3-D
In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.
On a Free Boundary Problem for a Nonlinear Coupled System of Evolution Equations of Oceanography.
On certain singular solutions of the partial differential equation... .
On Liouville theorem and the regularity of weak solutions to some nonlinear elliptic systems of higher order
The aim of this paper is to show that Liouville type property is a sufficient and necessary condition for the regularity of weak solutions of nonlinear elliptic systems of the higher order.
On periodic solutions of a special type of the beam equation
The paper deals with the existence of time-periodic solutions to the beam equation, in which terms expressing torsion and damping are also considered. The existence of periodic solutions is proved in the cas of time-periodic outer forces by means of an apriori estimate and the Fourier method.
On solvability of equations of the th order with jumping nonlinearities
On the complete integrability of an equation having solitons but not known to have a lax pair.
On the Existence of Solutions of Certain Asymptotically Homogeneous Problems.
On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order
On the regularity of solutions in Convex Integration theory.
On the stability of solitary waves for classical scalar fields
Ondes semi-linéaires conormales classiques par rapport à deux hypersurfaces transverses
Oscillation of solutions to a higher-order neutral PDE with distributed deviating arguments.