Layered solutions for a semilinear elliptic system in a ball

We consider the following system of Schrödinger-Poisson equations in the unit ball B₁ of R³:

     

Clustered spots in the FitzHugh-Nagumo system

We construct clustered spots for the following FitzHugh-Nagumo system:

     

Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect

We consider the elliptic-parabolic PDE system

     

Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model

We consider the classical parabolic-parabolic Keller-Segel system

     

Wave patterns, stability, and slow motions in inviscid and viscous hyperbolic equations with stiff reaction terms

We study the behavior of solutions to the inviscid (A=0) and the viscous (A>0) hyperbolic conservation laws with stiff source terms

     

Positive clustered layered solutions for the Gierer-Meinhardt system

We consider the stationary Gierer-Meinhardt system in a ball of RN:

     

New solutions for nonlinear Schrödinger equations with critical nonlinearity

We consider the following nonlinear Schrödinger equations in Rn

     

Regularity of invariant sets in semilinear damped wave equations

Under fairly general assumptions, we prove that every compact invariant subset I of the semiflow generated by the semilinear damped wave equation

     

Positive solutions to nonlinear p-Laplace equations with Hardy potential in exterior domains

We study the existence and nonexistence of positive (super)solutions to the nonlinear p-Laplace equation

     

Initial blow-up of solutions of semilinear parabolic inequalities

We study classical nonnegative solutions u(x,t) of the semilinear parabolic inequalities

     

Existence, uniqueness and blow-up rate of large solutions for a canonical class of one-dimensional problems on the half-line

This paper shows the existence and the uniqueness of the positive solution ?(t) of the singular boundary value problem

     

On the Cauchy problem for a reaction-diffusion equation with a singular nonlinearity

We consider the following Cauchy problem with a singular nonlinearity

(P)

     

Global existence and asymptotic behavior of solutions for nonlinear parabolic equations on unbounded domains

We study the existence and the asymptotic behavior of positive solutions for the parabolic equation on D×(0,∞), where is a some unbounded domain in and V belongs to a new parabolic class J^∞ of singular potentials generalizing the well-known parabolic Kato class at infinity P^∞ introduced recently by Zhang. We also show that the choice of this class is essentially optimal.     

Global branch from the second eigenvalue for a semilinear Neumann problem in a ball

Let (n?3) be a ball, and let f∈C³. We are concerned with the Neumann problem

     

Deduction of L. Hörmander's extension of Ásgeirsson's mean value theorem

L. Hörmander's extension of Ásgeirsson's mean value theorem states that if u is a solution of the inhomogeneous ultrahyperbolic equation (Δ_x−Δ_y)u=f, , , then