In this work we are interested in studying the existence of nontrivial weak solutions for a class of nonlinear elliptic equations defined in a bounded domain in dimension two, where the nonlinearities possess maximal exponential growth range motivated by Trudinger-Moser inequalities in Lorentz-Sobolev spaces. In order to study the solvability we use a variational approach. More specifically, we use mountain pass theorem combined with Trudinger-Moser type inequalities.

En este trabajo nos interesa estudiar la existencia de soluciones estacionarias para una ecuación de Navier-Stokes-3D en un fluido compresible e isotérmico. Para probar la existencia de soluciones usaremos un método de aproximaciones sucesivas, siguiendo los resultados mostrados por M. Padula.

In this work we are interested in studying the existence of nontrivial weak solutions for a class of nonlinear elliptic equations defined in a bounded domain in dimension two, where the nonlinearities possess maximal exponential growth range motivated by Trudinger-Moser inequalities in Lorentz-Sobolev spaces. In order to study the solvability we use a variational approach. More specifically, we use mountain pass theorem combined with Trudinger-Moser type inequalities.

In this work we are interested in studying the existence of stationary solutions for a Navier--Stokes--3D equation in a compressible and isothermal flow. In order to prove the existence of solutions we use a method of successive approximations, following the results shown by M. Padula.

Estudia ecuaciones elípticas de la forma (P) −∆u + λu = f(x, u), en Ω, u ∈ H1 0 (Ω), donde Ω ⊂ R N (N ≥ 2) es un dominio limitado o Ω = R N y f : Ω × R → R es una función continua con condiciones de crecimiento subcrítico y crítico. También estudia sistemas de ecuaciones elípticas de la forma (S)    −∆u = f(x, u, v), em Ω, −∆v = g(x, u, v), em Ω, u, v ∈ H1 0 (Ω), donde Ω ⊂ R N (N ≥ 2) , f, g : Ω × R 2 → R son funciones continuas con condiciones de crecimiento subcrítico. Encuentra soluciones definidas en H1 0 (Ω) × H1 0 (Ω), para sistemas elípticos de tipo gradiente y de tipo hamiltoniano. Para la existencia de soluciones usa Métodos Varacionales, haciendo uso especial del Teorema del Paso de Montaña.

This paper is devoted to showing the upper semicontinuity of global attractors associated with the family of nonlinear viscoelastic equations (Formula presented.) in a three-dimensional space, for f growing up to the critical exponent and dependent on ρ ∈ [0,4), as ρ→0+. This equation models extensional vibrations of thin rods with nonlinear material density ϱ(∂tu) = |∂tu|ρ and presence of memory effects. This type of problems has been extensively studied by several authors; the existence of a global attractor with optimal regularity for each ρ ∈ [0,4) were established only recently. The proof involves the optimal regularity of the attractors combined with Hausdorff's measure.

The main objective of this work is to study the long-term dynamics of a p−Kirchhoff model with infinite memory exposed to structural forces on a bounded domain Ω ⊂ ℝn. In particular, the existence of a global attractor with exponential attraction rate and finite fractal dimension is shown, that is, the existence of an exponential attractor is proved.