On a maximum principle for nonlinear equations
On a method for solving a classical variational problem.
On a Method of K. Uhlenbeck for Proving Partial Regularity for Solutions of Certain Nonlinear Elliptic Systems.
On a min-max procedure for the existence of a positive solution for certain scalar field equations in RN.
In this paper we mainly introduce a min-max procedure to prove the existence of positive solutions for certain semilinear elliptic equations in RN.
On a model of rotating superfluids
We consider an energy-functional describing rotating superfluids at a rotating velocity , and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical above which energy-minimizers have vortices, evaluations of the minimal energy as a function of , and the derivation of a limiting free-boundary problem.
On a model of rotating superfluids
We consider an energy-functional describing rotating superfluids at a rotating velocity ω, and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical ω above which energy-minimizers have vortices, evaluations of the minimal energy as a function of ω, and the derivation of a limiting free-boundary problem.
On a multilevel Krylov method for the Helmholtz equation preconditioned by shifted Laplacian.
On a non linear partial differential equation having natural growth terms and unbounded solution
On a nonlinear eigenvalue problem in Sobolev spaces with variable exponent.
On a nonlinear elliptic boundary value problem
On a nonlinear elliptic system: resonance and bifurcation cases
In this paper we consider an elliptic system at resonance and bifurcation type with zero Dirichlet condition. We use a Lyapunov-Schmidt approach and we will give applications to Biharmonic Equations.
On a nonlinear problem modelling states of thermal equilibrium of superconductors.
On a nonlinear stationary problem in unbounded domains.
We study existence and some properties of solutions of the nonlinear elliptic equation N(x,a(u))Lu = f in unbounded domains. The above method is not a variational problem. Our techniques involve fixed point arguments and Galerkin method.
On a nonlocal eigenvalue problem
On a nonlocal elliptic problem
We study stationary solutions of the system , m => 1, Δφ = ±u, defined in a bounded domain Ω of . The physical interpretation of the above system comes from the porous medium theory and semiconductor physics.
On a nonresonance condition between the first and the second eigenvalues for the -Laplacian.
On a non-self adjoint eigenfunction expansion.
On a parallel implementation of the mortar element method
On a Parallel Implementation of the Mortar Element Method
We discuss a parallel implementation of the domain decomposition method based on the macro-hybrid formulation of a second order elliptic equation and on an approximation by the mortar element method. The discretization leads to an algebraic saddle- point problem. An iterative method with a block- diagonal preconditioner is used for solving the saddle- point problem. A parallel implementation of the method is emphasized. Finally the results of numerical experiments are presented.
On a perturbed Dirichlet problem for a nonlocal differential equation of Kirchhoff type.