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

     

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

We consider the following Cauchy problem with a singular nonlinearity

(P)

     

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

     

New solutions for nonlinear Schrödinger equations with critical nonlinearity

We consider the following nonlinear Schrödinger equations in Rn

     

Uniqueness properties of solutions of Schrödinger equations

Under suitable assumptions on the potentials V and a, we prove that if u∈C([0,1],H¹) is a solution of the linear Schrödinger equation

     

Positive clustered layered solutions for the Gierer-Meinhardt system

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

     

On positive solutions concentrating on spheres for the Gierer-Meinhardt system

We consider the stationary Gierer-Meinhardt system in a ball of R^N:

     

Dynkin's formula and large coupling convergence

Let H?1 be a selfadjoint operator in H, let J be a linear and bounded operator from (D(H^1/2),∥H^1/2·∥) to H_aux and for β>0 let be the nonnegative selfadjoint operator in H satisfying

     

Multiple positive solutions for a quasilinear elliptic equation with critical exponential nonlinearity

Let Ω be a bounded domain in R^N,N≥2, with C² boundary. In this work, we study the existence of multiple positive solutions of the following problem:

     

Initial blow-up of solutions of semilinear parabolic inequalities

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

     

Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type

We find for small ε positive solutions to the equation