Global solutions for a nonlinear wave equation with the p-laplacian operator

H. Gao, Institute of Applied Physics and Computational Mathematics, Beijing, China
T. F. Ma, Universidade Estadual de Maringá, Maringá, Brazil

E. J. Qualitative Theory of Diff. Equ., No. 11. (1999), pp. 1-13.

Communicated by Bo Zhang. Appeared on 1999-01-01

Abstract: We study the existence and asymptotic behavior of the global solutions of the nonlinear equation
$$u_tt-\Delta_p u+(-\Delta)^\alpha u_t+g(u)=f$$
where $0<alpha\leq 1$ and $g$ does not satisfy the sign condition $g(u)u \geq 0$.

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