On the spectrum of the -Laplacian operator for Neumann eigenvalue problems with weights.
On the stability of difference schemes for nonlinear elliptic differential equations with boundary conditions of Dirichlet type
On the stability of solutions of nonlinear parabolic differential-functional equations
We consider a nonlinear differential-functional parabolic boundary initial value problem (1) ⎧A z + f(x,z(t,x),z(t,·)) - ∂z/∂t = 0 for t > 0, x ∈ G, ⎨z(t,x) = h(x) for t > 0, x ∈ ∂G, ⎩z(0,x) = φ₀(x) for x ∈ G, and the associated elliptic boundary value problem with Dirichlet condition (2) ⎧Az + f(x,z(x),z(·)) = 0 for x ∈ G, ⎨z(x) = h(x) for x ∈ ∂G ⎩ where , G is an open and bounded domain with (0 < α ≤ 1) boundary, the operator Az := ∑j,k=1m ajk(x) (∂²z/(∂xj ∂xk)) is...
On the unique solvability of nonresonant elliptic equations
On the unique solvability of semi-linear elliptic systems
On two problems studied by A. Ambrosetti
We study the Ambrosetti–Prodi and Ambrosetti–Rabinowitz problems.We prove for the first one the existence of a continuum of solutions with shape of a reflected (-shape). Next, we show that there is a relationship between these two problems.
On Two-Dimensional Quasi-Linear Elliptic Systems.
On uniqueness conditions for decreasing solutions of semilinear elliptic equations.
On Uniqueness of Boundary Values of Solutions of a Problem Arising in Plasma Physics.
Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity
Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity
We study here an optimal control problem for a semilinear elliptic equation with an exponential nonlinearity, such that we cannot expect to have a solution of the state equation for any given control. We then have to speak of pairs (control, state). After having defined a suitable functional class in which we look for solutions, we prove existence of an optimal pair for a large class of cost functions using a non standard compactness argument. Then, we derive a first order optimality system assuming...
Optimal Lyapunov inequalities and applications to nonlinear problems
Optimal regularity for codimension one minimal surfaces with a free boundary.
Optimisation de forme et problème à frontière libre : cas du p-laplacien
Oscillation of the solution to a singular differential equation.