Solutions to nonlinear elliptic equations with a nonlocal boundary condition.
Solutions to perturbed eigenvalue problems of the -Laplacian in .
Solutions to some nonlinear PDE's in the form of Laplace type integrals
A nonlinear equation in 2 variables is considered. A formal solution as a series of Laplace integrals is constructed. It is shown that assuming some properties of Char P, one gets the Gevrey class of such solutions. In some cases convergence “at infinity” is proved.
Solutions to stationary phase-field equations.
Solutions to the equation div u = f in weighted Sobolev spaces
We consider the problem div u = f in a bounded Lipschitz domain Ω, where f with is given. It is shown that the solution u, constructed as in Bogovski’s approach in [1], fulfills estimates in the weighted Sobolev spaces , where the weight function w is in the class of Muckenhoupt weights .
Solutions to the mean curvature equation by fixed point methods.
Solutions to three-dimensional Navier-Stokes equations for incompressible fluids.
Solutions to time-fractional diffusion-wave equation in cylindrical coordinates.
Solutions which are flat or Singular on Totally Characteristic Manifolds of first order Partial Differential Equations
Solutions with prescribed periods on the boundary components on non-linear elliptic systems of first order in multiply connected domains in the plane
Solutions with subgroup symmetry for singular equations in bifurcation theory.
Solutions with vortices of a semi-stiff boundary value problem for the Ginzburg–Landau equation
We study solutions of the 2D Ginzburg–Landau equation subject to “semi-stiff” boundary conditions: Dirichlet conditions for the modulus, , and homogeneous Neumann conditions for the phase. The principal result of this work shows that there are stable solutions of this problem with zeros (vortices), which are located near the boundary and have bounded energy in the limit of small . For the Dirichlet boundary condition (“stiff” problem), the existence of stable solutions with vortices, whose energy...
Soluzioni di tipo barriera
We present the general theory of barrier solutions in the sense of De Giorgi, and we consider different applications to ordinary and partial differential equations. We discuss, in particular, the case of second order geometric evolutions, where the barrier solutions turn out to be equivalent to the well-known viscosity solutions.
Soluzioni di viscosità
This is the expanded text of a lecture about viscosity solutions of degenerate elliptic equations delivered at the XVI Congresso UMI. The aim of the paper is to review some fundamental results of the theory as developed in the last twenty years and to point out some of its recent developments and applications.
Soluzioni di viscosità e stabilità per equazioni completamente nonlineari
Soluzioni periodiche di PDEs Hamiltoniane
Presentiamo nuovi risultati di esistenza e molteplicità di soluzioni periodiche di piccola ampiezza per equazioni alle derivate parziali Hamiltoniane. Otteniamo soluzioni periodiche di equazioni «completamente risonanti» aventi nonlinearità generali grazie ad una riduzione di tipo Lyapunov-Schmidt variazionale ed usando argomenti di min-max. Per equazioni «non risonanti» dimostriamo l'esistenza di soluzioni periodiche di tipo Birkhoff-Lewis, mediante un'opportuna forma normale di Birkhoff e realizzando...
Solvability and asymptotics of solutions of crack-type boundary-contact problems of the ocuple-stress elasticity.
Solvability and bifurcations of some strongly nonlinear equations
Solvability Conditions for a Linearized Cahn-Hilliard Equation of Sixth Order
We obtain solvability conditions in H6(ℝ3) for a sixth order partial differential equation which is the linearized Cahn-Hilliard problem using the results derived for a Schrödinger type operator without Fredholm property in our preceding article [18].
Solvability for a class of non-homogeneous differential operators on two-step nilpotent groups.