Schrödinger equations with unique positive isolated singularities.
Schrödingers Operators with Singular Magnetic Vector Potentials.
Second-order boundary estimates for solutions to singular elliptic equations.
Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order
Semilinear geometric optics for generalized solutions.
Sign changing solutions for elliptic equations with critical growth in cylinder type domains
We prove the existence of positive and of nodal solutions for , , where and , for a class of open subsets of lying between two infinite cylinders.
Sign changing solutions for elliptic equations with critical growth in cylinder type domains
We prove the existence of positive and of nodal solutions for -Δu = |u|p-2u + µ|u|q-2u, , where µ > 0 and 2 < q < p = 2N(N - 2) , for a class of open subsets Ω of lying between two infinite cylinders.
Sign-changing and multiple solutions for the -Laplacian.
Similarity stabilizes blow-up
The blow-up of solutions to a quasilinear heat equation is studied using a similarity transformation that turns the equation into a nonlocal equation whose steady solutions are stable. This allows energy methods to be used, instead of the comparison principles used previously. Among the questions discussed are the time and location of blow-up of perturbations of the steady blow-up profile.
Singularity patterns in a chemotaxis model.
Slowly oscillating solutions of a parabolic inverse problem: boundary value problems.
Solutions of type for a class of singular equations.
Solutions oscillantes des équations de Carleman
Some elementary inequalities in gas dynamics equation.
Some existence results for the scalar curvature problem via Morse theory
We prove existence of positive solutions for the equation on , arising in the prescribed scalar curvature problem. is the Laplace-Beltrami operator on , is the critical Sobolev exponent, and is a small parameter. The problem can be reduced to a finite dimensional study which is performed with Morse theory.
Some new oscillation criteria for second order elliptic equations with damping
Some new oscillation criteria are obtained for second order elliptic differential equations with damping , x ∈ Ω, where Ω is an exterior domain in ℝⁿ. These criteria are different from most known ones in the sense that they are based on the information only on a sequence of subdomains of Ω ⊂ ℝⁿ, rather than on the whole exterior domain Ω. Our results are more natural in view of the Sturm Separation Theorem.
Some properties of solutions for the generalized thin film equation in one space dimension.
Some Regularity Results for Quasilinear Elliptic Systems of Second Order.
Some results about blow-up and global existence to a semilinear degenerate heat equation.
Some theorems on partial differential inequalities of parabolic type