Scholarlink

<p>We study a boundary-value problem with asymmetric time conditions for a third-order inhomogeneous equation with multiple characteristics of lowest-order terms. The unique solvability of the problem is proved by the energy-integral method. It is shown that if the uniqueness condition is violated, then the homogeneous problem has a nontrivial solution. The existence is proved by the Fourier method. The solution of the stated problem is obtained in the explicit form by using the constructed Green’s function. The uniform convergence of the solutions and their derivatives contained in the equation is proved.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Solutions of a Time-Asymmetric Boundary-Value Problem for a Third-Order Equation with Variable Coefficients

  • 期刊论文

  • 发表日期：

    2026年2月1日

查看全文
  • Yusupjon Apakov,
  • Raxmatilla Umarov

摘要

We study a boundary-value problem with asymmetric time conditions for a third-order inhomogeneous equation with multiple characteristics of lowest-order terms. The unique solvability of the problem is proved by the energy-integral method. It is shown that if the uniqueness condition is violated, then the homogeneous problem has a nontrivial solution. The existence is proved by the Fourier method. The solution of the stated problem is obtained in the explicit form by using the constructed Green’s function. The uniform convergence of the solutions and their derivatives contained in the equation is proved.