Solutions to the mean curvature equation by fixed point methods.
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 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 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.
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 semilinear PDE with multiple characteristics
We prove local solvability in Gevrey spaces for a class of semilinear partial differential equations. The linear part admits characteristics of multiplicity k ≥ 2 and data are fixed in , 1 < σ < k/(k-1). The nonlinearity, containing derivatives of lower order, is assumed of class with respect to all variables.
Solvability of degenerate elliptic boundary value problems: another approach
Using a Hardy-type inequality, the authors weaken certain assumptions from the paper [1] and derive existence results for equations with a stronger degeneration.
Solvability of linear and semilinear eigenvalue problems with data
Solvability of nonlinear Dirichlet problem for a class of degenerate elliptic equations.
Solvability of nonlinear problems at resonance
Solvability of quasilinear elliptic equations with strong dependence on the gradient.
Solvability of semilinear equations with strong nonlinearities and applications to elliptic boundary value problems
Solvability of the Dirichlet problem for elliptic equations in weighted Sobolev spaces on unbounded domains.
Solvability of the Poisson equation in weighted Sobolev spaces
The aim of this paper is to prove the existence of solutions to the Poisson equation in weighted Sobolev spaces, where the weight is the distance to some distinguished axis, raised to a negative power. Therefore we are looking for solutions which vanish sufficiently fast near the axis. Such a result is useful in the proof of the existence of global regular solutions to the Navier-Stokes equations which are close to axially symmetric solutions.
Solvability of the superlinear elliptic boundary value problem
Solving heat and wave-like equations using He's polynomials.
Solving Large Nonlinear Systems of Equations by an Adaptive Condensation Process.
Solving -Laplacian equations on complete manifolds.
Solving the Dirichlet acoustic scattering problem for a surface with added bumps using the Green's function for the original surface.
Solving the multidimensional difference biharmonic equation by the Monte Carlo method.