Abstract
A nonlinear time-fractionally damped wave equation with an inverse-square potential posed on the interval (0, 1) is investigated. The time-fractionally derivative is considered in the Caputo sense. A weight function of the form x −σ ( σ∈R ) is allowed in front of the nonlinearity ∣u(t, x)∣ p (p > 1). The problem is studied under certain initial conditions and a homogeneous boundary condition. Namely, we obtain sufficient conditions under which the considered problem admits no weak solution. The cases u(0, · ) ≡ 0 and u(0, · ) ≢ 0 are studied separately.
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