Displaying similar documents to “Some results on semilinear systems on the unbounded space R3.”

Global existence and decay of solutions of a coupled system of BBM-Burgers equations.

Jardel Morais Pereira (2000)

Revista Matemática Complutense

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The global well-posedness of the initial-value problem associated to the coupled system of BBM-Burgers equations (*) in the classical Sobolev spaces H(R) x H(R) for s ≥ 2 is studied. Furthermore we find decay estimates of the solutions of (*) in the norm L(R) x L(R), 2 ≤ q ≤ ∞ for general initial data. Model (*) is motivated by a work due to Gear and Grimshaw [10] who considered strong interaction of weakly nonlinear long waves governed by a coupled system of KdV equations.

A Dirichlet problem with asymptotically linear and changing sign nonlinearity.

Marcello Lucia, Paola Magrone, Huan-Song Zhou (2003)

Revista Matemática Complutense

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This paper deals with the problem of finding positive solutions to the equation -∆[u] = g(x,u) on a bounded domain 'Omega' with Dirichlet boundary conditions. The function g can change sign and has asymptotically linear behaviour. The solutions are found using the Mountain Pass Theorem.