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Keywords:
nonlinear problem; existence of solutions; Galerkin method; compactness; pseudo-Laplacian; asymptotic behaviour; energy type estimates
nonlinear problem; existence of solutions; Galerkin method; compactness; pseudo-Laplacian; asymptotic behaviour; energy type estimates
Summary:
We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for \begin{align*} &u^{\prime\prime} + Au - \Delta u^\prime + |v|^{\rho +2}\,|u|^\rho \,u = f_1\\ &v^{\prime\prime} + Av - \Delta v^\prime + |u|^{\rho +2}\,|v|^\rho \,v = f_2 \tag{*}\end{align*} where $A$ is the pseudo-Laplacian operator.
References:
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