En el presente trabajo de Investigación se demuestra la existencia de solución de un sistema acoplado no lineal en espacios de Sobolev, mas precisamente dicho sistema involucra ecuaciones diferenciales parciales del tipo elíptico no lineal: ∆ 2�������� − √��������1∆�������� + ��������1�������� = ��������1�������� 3 + ����������������(��������, ��������) ∆ 2�������� − √��������1∆�������� + ��������1�������� = ��������1�������� 3 + ����������������(��������, ��������) Donde, �������� y ��������...

In the system (*), with Neumann boundary conditions and locally distributed dissipation; where a (x) ≥ a0 >0 a.e.in ω, ωΩ neighborhood 0f Γ= ∂Ω which is an open problem, see [6], we study the asymptotic behavior.

In the system (*), with Neumann boundary conditions and locally distributed dissipation; where a (x) ≥ a0 >0 a.e.in ω, ωΩ neighborhood 0f Γ= ∂Ω which is an open problem, see [6], we study the asymptotic behavior.

In this note we shall study the asymptotic behavior of the wave equation with boundary condition of Newmann type, locally distributed. Using the Principle of the Unique Continuation, result studied by Ruiz (5) and applied to problems of asymptotic behavior by Zuazua (6).

Se estudia el comportamiento asintótico de la ecuación de onda con condición de frontera del tipo Newmann, localmente distribuido. Empleando el Principio de la Continuación Única, resultado estudiado por Ruíz (5) y aplicado a problemas de comportamiento asintótico por Zuazua (6).

The objective of this work is to obtain weak solutions for a type of problem of type p(x) - Kirchhoff. The result is obtained by Fredholm-type results for a pair of non-linear operators. In addition, the uniqueness of weak solutions is considered.