Positive solutions of an elliptic equation with strongly nonlinear lower order terms.
Régularité de la solution d’une équation fortement (ou faiblement) non linéaire dans
Résultats d'existence et de non-existence pour la solution positive et bornée d'une e.d.p. elliptique non linéaire
Supersolutions and stabilization on the solution of a nonlinear parabolic system.
Existence and nonexistence of nontrivial solutions for some nonlinear elliptic systems.
In this paper we give some existence and nonexistence results of non trivial solutions of nonlinear elliptic systems involving the p-Laplacian.
Non résonance près de la première valeur propie d'un système elliptique quasilinéaire de type potentiel.
Supersolutions and stabilization of the solutions of the equation∂u/∂t - div(|∇p| ∇u) = h(x,u), Part II.
In this paper we consider a nonlinear parabolic equation of the following type: (P) ∂u/∂t - div(|∇p|p-2 ∇u) = h(x,u) with Dirichlet boundary conditions and initial data in the case when 1 < p < 2. We construct supersolutions of (P), and by use of them, we prove that for tn → +∞, the solution of (P) converges to some solution of the elliptic equation associated with (P).
On the existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems.
We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the inverse of the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.
Asymptotic behavior of solutions for some nonlinear partial differential equations on unbounded domains.
Four-parameter bifurcation for a -Laplacian system.
Boundary behavior and estimates for solutions of equations containing the -Laplacian.
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