An incorrectly posed problem for nonlinear elliptic equations.
Annulus oscillation criteria for second order nonlinear elliptic differential equations with damping.
Applications of geometric measure theory to the study of Gauss- Weierstrass and Poisson integrals.
Arbitrary growth and oscillation versus finite time blow up in nonlinear Schrödinger equations
Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems
We consider the semilinear Lane–Emden problem where and is a smooth bounded domain of . The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of , as . Among other results we show, under some symmetry assumptions on , that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as , and the limit profile looks like a tower of two bubbles given by a superposition of a regular and a singular solution of the Liouville...
Asymptotic behavior of a predator-prey diffusion system with time delays.
Asymptotic behaviour for the solution of the compressible Navier-Stokes equation, when the compressibility goes to zero
Asymptotic behaviour of solutions of some semilinear parabolic problems
Asymptotic behaviour of the solutions of a strongly nonlinear parabolic problem
Asymptotic estimates for PDE with -Laplacian and damping.
Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball.
Asymptotics for quasilinear equations with nearly critical growth.
Asymptotics of parabolic equations with possible blow-up
We describe the long-time behaviour of solutions of parabolic equations in the case when some solutions may blow up in a finite or infinite time. This is done by providing a maximal compact invariant set attracting any initial data for which the corresponding solution does not blow up. The abstract result is applied to the Frank-Kamenetskii equation and the N-dimensional Navier-Stokes system with small external force.
Asymptotics of the first nodal line
Asymptotics of the Nodal Lines of Solutions of 2-Dimensional Schrödinger Equations.
Averaging techniques and oscillation of quasilinear elliptic equations
By using averaging techniques, some oscillation criteria for quasilinear elliptic differential equations of second order are obtained. These results extend and generalize the criteria for linear differential equations due to Kamenev, Philos and Wong.
Behaviour of symmetric solutions of a nonlinear elliptic field equation in the semi-classical limit: Concentration around a circle.
"Best possible'' maximum principles
Blow-up behavior in nonlocal vs local heat equations
We present some recent results on the blow-up behavior of solutions of heat equations with nonlocal nonlinearities. These results concern blow-up sets, rates and profiles. We then compare them with the corresponding results in the local case, and we show that the two types of problems exhibit "dual" blow-up behaviors.
Blowup estimates for a mutualistic model in ecology.