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Existence and Uniqueness of Solutions
Existence and Uniqueness of Solutions continued
Linear Differential Equations
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adjoint analytic assumed asymptotic boundary condition boundary-value problem Chap characteristic roots class C1 Clearly coefficients column completes the proof components considered constant matrix continuous function convergent corresponding critical points defined denoted derivatives determined diagonal matrix differential equation domain eigenfunctions eigenvalues elements entire function equicontinuous finite number fixed formal series formal solution fundamental matrix given Green's formula Green's function hence Hint holds implies inequality interval Jacobian L(C+ Lemma limit limit-point linear system linearly independent linearly independent solutions nonsingular matrix Parseval equality periodic orbit periodic solution plane polynomial Prob problem Lx proof of Theorem regular singular point result satisfies self-adjoint sequence Show shown solution of 1.1 solutions of Lx successive approximations sufficiently large Suppose tends Theorem 2.1 tion uniform convergence unique solution valid vanish vector yields