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- W2055557910 abstract "This chapter discusses the existence of real numbers λ i such that a solution x (λ, t) on 0 x ″ + x F(x, λ, t) = 0 satisfies initial conditions. The chapter presents the theorem—Let D be the set {( x , λ, t) : — ∞ x x , hypothesis fourth is satisfied. Thus, this hypothesis has been viewed as describing or restraining the nonlinearity of equations. Thus, by lengthening the arguments to follow one may show that hypotheses third and fourth need only hold for large λ. Both of these hypotheses allow a pleasant physical interpretation if F in initial equation is viewed as a spring constant. For every non-negative integer n and every positive number p , there exists a λ pn and a solution x (λ pn , t, p) of Ρ having n zeros in (0, 1) and such that x′(λ pn , 0, p) = p . Furthermore, for each n there exists a particular p = p (n) such that the sequence of solutions {x (λ Ρ (n)n , t>p( n ))} admits a sequence {y n (t)} together with which it forms a complete biorthogonal system in L 2 ([0 1])." @default.
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- W2055557910 date "1962-03-01" @default.
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- W2055557910 title "A class of characteristic-value problems" @default.
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