Existence and asymptotic behaviour of solutions of a nonlinear evolution problem
Nelson Nery de Oliveira Castro · Applications of Mathematics · 1997
We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for $$\left\{ \begin{gathered} u\prime\prime + Au - \Delta u\prime + |v|^{\varrho + 2} |u|^\varrho u = f_1 \hfill \\ v\prime\prime + Au - \Delta u\prime + |u|^{\varrho + 2} |v|^\varrho v = f_2 \hfill \\ \end{gathered} \right.$$ where A is the pseudo-Laplacian operator.