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Second-order maximum principle controlled weakly singular Volterra integral equations

Jasarat J. Gasimov, Nazim I. Mahmudov

Abstract

This work studies a class of singular Volterra integral equations that are (controlled) and can be applied to memory-related problems.For optimum controls, we prove a second-order Pontryagin type maximal principle.

Second-order maximum principle controlled weakly singular Volterra integral equations

Abstract

This work studies a class of singular Volterra integral equations that are (controlled) and can be applied to memory-related problems.For optimum controls, we prove a second-order Pontryagin type maximal principle.
Paper Structure (3 sections, 3 theorems, 40 equations)

This paper contains 3 sections, 3 theorems, 40 equations.

Table of Contents

  1. Introduction.
  2. Main Result.
  3. Proof of the theorem.

Key Result

Theorem 2.1

Let $(A1)$ and $(A2)$ hold. Let $\eta(\cdot)\in L(0,T;R^{n})$ and $\eta(\cdot)$ be continuous at $t_{j}, j=1,2,\cdots,m.$ Suppose $(y^{*}(\cdot),u^{*}(\cdot))$ is an optimal pair of $1-2$. Then there a solution $\psi(\cdot)\in L^{\frac{p}{p-1}}(0,T;R^{n})$ of the following adjoint equation such that following estimation holds: where

Theorems & Definitions (5)

  • Definition 2.1
  • Theorem 2.1
  • Lemma 2.1
  • Lemma 2.2
  • Example 2.1