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The article is devoted to the study of problems of finding the non-negative coefficient q(t) in the elliptic equation utt + a2Δu − q(t)u = f(x, t) (x = (x1, . . . , xn) ∈ Ω ⊂ Rn, t ∈ (0, T), 0 &lt; T &lt; +∞, Δ — operator Laplace on x1, . . . , xn). These problems contain the usual boundary conditions and additional condition ( spatial integral overdetermination condition or boundary integral overdetermination condition). The theorems of existence and uniqueness are proved

Inverse Problems of Finding the Lowest Coefficient in the Elliptic Equation