Let G be a given bounded domain in R, I be the boundary of G, G...

Transcribed Image Text:

Let G be a given bounded domain in R", I be the boundary of G, G = GUT: f(r) E C(G), g(y) € C(G), F(1) € C(G) be given functions. Let us consider the Fredholm integral equation of the second kind (x) = A f(2)g(4)<(y)dy+ F(x). (3) a)Find the integral equation which adjoint to (3). Find eigenvalues and corresponding them eigenfunctions of the homogeneous adjoint integral equation. b) Let A(2)g(z)dr 1. Find the necessary and sufficient conditions for existence of a solut ion of (3) and find all solutions of (3) . Let G be a given bounded domain in R", I be the boundary of G, G = GUT: f(r) E C(G), g(y) € C(G), F(1) € C(G) be given functions. Let us consider the Fredholm integral equation of the second kind (x) = A f(2)g(4)<(y)dy+ F(x). (3) a)Find the integral equation which adjoint to (3). Find eigenvalues and corresponding them eigenfunctions of the homogeneous adjoint integral equation. b) Let A(2)g(z)dr 1. Find the necessary and sufficient conditions for existence of a solut ion of (3) and find all solutions of (3) .