Exercise 3.6 The following integral equation for f: [-a, a] R arises in a model...

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Exercise 3.6 The following integral equation for f: [-a, a] → R arises in a model of the motion of gas particles on a line: f(x) = 1 + = - - ₁ ㅠ 1 1 + (x − y)² f (y) dy for -a ≤ x ≤a. Prove that this equation has a unique bounded, continuous solution for every 0 < a < x. Prove that the solution is nonnegative. What can you say if a = ∞? Exercise 3.6 The following integral equation for f: [-a, a] → R arises in a model of the motion of gas particles on a line: f(x) = 1 + = - - ₁ ㅠ 1 1 + (x − y)² f (y) dy for -a ≤ x ≤a. Prove that this equation has a unique bounded, continuous solution for every 0 < a < x. Prove that the solution is nonnegative. What can you say if a = ∞?