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<p>We study the unique solvability of a linear differential equation with the Liouville derivative and a bounded operator <i>A</i>, where the equation is considered on the real axis without initial conditions. Using the two-sided Laplace transform, we establish the existence and uniqueness of a solution in the spaces of continuously differentiable and exponentially bounded functions. The solution is represented as the convolution of the inverse Laplace transform of the resolvent of <i>A</i> with the right-hand side. The results are applied to linear systems of ordinary differential equations with a degenerate matrix at the Liouville derivative and the boundary value problem for a pseudoparabolic equation in both nondegenerate and degenerate cases. Bibliography: 14 titles.</p>

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EQUATIONS WITH LIOUVILLE DERIVATIVE AND TWO-SIDED LAPLACE TRANSFORM

  • 期刊论文

  • 发表日期：

    2026年5月26日

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  • V. E. Fedorov,
  • N. M. Skripka

摘要

We study the unique solvability of a linear differential equation with the Liouville derivative and a bounded operator A, where the equation is considered on the real axis without initial conditions. Using the two-sided Laplace transform, we establish the existence and uniqueness of a solution in the spaces of continuously differentiable and exponentially bounded functions. The solution is represented as the convolution of the inverse Laplace transform of the resolvent of A with the right-hand side. The results are applied to linear systems of ordinary differential equations with a degenerate matrix at the Liouville derivative and the boundary value problem for a pseudoparabolic equation in both nondegenerate and degenerate cases. Bibliography: 14 titles.