Generalized Picone and Riccati inequalities for half-linear differential operators with arbitrary elliptic matrices.
Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential
We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of -Laplacian type. If and the right-hand side is a Radon measure with singularity of order at , then any supersolution in has singularity of order at least at . In the proof we exploit a pointwise estimate of -superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff’s potential of Radon’s measure.
Geometrical properties of the solutions of one-dimensional nonlinear parabolic equations.
Geometry of stationary sets for the wave equation in . The case of finitely supported initial data: An announcement.
Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators
The problems of Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators are studied by several authors (see [1]–[5]). In this paper we obtain the Gevrey hypoellipticity for a degenerated quasi-elliptic operator in , without any restriction on the characteristic polyhedron.
Global attractivity, oscillation and Hopf bifurcation for a class of diffusive hematopoiesis models
In this paper, we discuss the special diffusive hematopoiesis model with Neumann boundary condition. Sufficient conditions are provided for the global attractivity and oscillation of the equilibrium for Eq. (*), by using a new theorem we stated and proved. When P(t, χ) does not depend on a spatial variable χ ∈ Ω, these results are also true and extend or complement existing results. Finally, existence and stability of the Hopf bifurcation for Eq. (*) are studied.
Global behaviour of solutions to some nonlinear diffusion equations
Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations
We examine the parabolic system of three equations - Δu = , - Δv = , - Δw = , x ∈ , t > 0 with p, q, r positive numbers, N ≥ 1, and nonnegative, bounded continuous initial values. We obtain global existence and blow up unconditionally (that is, for any initial data). We prove that if pqr ≤ 1 then any solution is global; when pqr > 1 and max(α,β,γ) ≥ N/2 (α, β, γ are defined in terms of p, q, r) then every nontrivial solution exhibits a finite blow up time.
Global Hölder estimates for equations of Monge-Ampère type.
Global Instability and Essential Spectrum in Semilinear Evolution Equations.
Global solutions and quenching to a class of quasilinear parabolic equations.
Global subanalytic solutions of Hamilton–Jacobi type equations
Gradient bounds and Liouville theorems for quasilinear elliptic equations
Grandient Estimates for Degenerate Diffusion Equations. I.
Ground states of nonlinear Schrödinger equations with potentials