In this paper Lp Lq estimates for the solution u(x,t) to the following perturbed higher order hyperbolic equation are considered,(οtt-aΔ)(οtt-bΔ)u+V(x)u=0,\ x∈Rn,n≥6, οjtu(x,0)=0,\ ο3tu(x,0)=f(x),\ (j=0,1,2).W...In this paper Lp Lq estimates for the solution u(x,t) to the following perturbed higher order hyperbolic equation are considered,(οtt-aΔ)(οtt-bΔ)u+V(x)u=0,\ x∈Rn,n≥6, οjtu(x,0)=0,\ ο3tu(x,0)=f(x),\ (j=0,1,2).We assume that the potential V(x) and the initial data f(x) are compactly supported, and V(x) is sufficiently small, then the solution u(x,t) of the above problem satisfies the same Lp Lq estimates as that of the unperturbed problem. Received November 25,1996. Revised April 14,1997.1991 MR Subject Classification:35L05,35B20,35B45.展开更多
文摘In this paper Lp Lq estimates for the solution u(x,t) to the following perturbed higher order hyperbolic equation are considered,(οtt-aΔ)(οtt-bΔ)u+V(x)u=0,\ x∈Rn,n≥6, οjtu(x,0)=0,\ ο3tu(x,0)=f(x),\ (j=0,1,2).We assume that the potential V(x) and the initial data f(x) are compactly supported, and V(x) is sufficiently small, then the solution u(x,t) of the above problem satisfies the same Lp Lq estimates as that of the unperturbed problem. Received November 25,1996. Revised April 14,1997.1991 MR Subject Classification:35L05,35B20,35B45.
