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

     

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

     

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

     

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

     

New solutions for nonlinear Schrödinger equations with critical nonlinearity

We consider the following nonlinear Schrödinger equations in Rn

     

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

     

A new partial regularity result for non-autonomous convex integrals with non-standard growth conditions

We establish C1,γ-partial regularity of minimizers of non-autono-mous convex integral functionals of the type: , with non-standard growth conditions into the gradient variable

     

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 positive solutions concentrating on spheres for the Gierer-Meinhardt system

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

     

Asymptotic behaviour of principal eigenvalues for a class of cooperative systems

This paper analyzes the asymptotic behaviour as λ↑∞ of the principal eigenvalue of the cooperative operator

     

Positive clustered layered solutions for the Gierer-Meinhardt system

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

     

A complete classification of bifurcation diagrams of classes of multiparameter p-Laplacian boundary value problems

We study the bifurcation diagrams of positive solutions of the multiparameter p-Laplacian problem

     

“Bubble-tower” radial solutions in the slightly supercritical Brezis-Nirenberg problem

In this paper, we consider the Brezis-Nirenberg problem in dimension N?4, in the supercritical case. We prove that if the exponent gets close to and if, simultaneously, the bifurcation parameter tends to zero at the appropriate rate, then there are radial solutions which behave like a superposition of bubbles, namely solutions of the form