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

We consider the following Cauchy problem with a singular nonlinearity

(P)

     

Well-posedness results for triply nonlinear degenerate parabolic equations

We study well-posedness of triply nonlinear degenerate elliptic-parabolic-hyperbolic problems of the kind

     

Positive solutions of an elliptic equation with negative exponent: Stability and critical power

We study positive solutions of the equation

     

Existence of nonnegative solutions for a class of semilinear elliptic systems with indefinite weight

We prove the existence of nonnegative solutions to the system

     

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

     

Global existence and maximal regularity of solutions of gradient systems

In this article, we use a Galerkin method to prove a maximal regularity result for the following abstract gradient system

     

Ground states of a prescribed mean curvature equation

We study the existence of radial ground state solutions for the problem

     

The mixed problem for the Lamé system in a class of Lipschitz domains

We consider the mixed problem for the Lamé system

     

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:

     

On the Cauchy problem for the fast diffusion equation

For , the author studies the existence of a kind of weak solution to the Cauchy problem