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Kneser Solutions of Higher-Order Quasilinear Ordinary Differential Equations
Funkcialaj Ekvacioj, 2022Manabu Naito, Hiroyuki Usami
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Analysis, 1984
The author considers a Volterra operator \(S: M\to C=C([0,T],E)\), where E is a Banach space and M is a subset of C and shows that the set L of all fixed points of S can be represented by an iteration formula using certain mappings defined by S. Under an asymptotic compactness hypothesis it is proved that L is nonempty, compact and if M is connected, L
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The author considers a Volterra operator \(S: M\to C=C([0,T],E)\), where E is a Banach space and M is a subset of C and shows that the set L of all fixed points of S can be represented by an iteration formula using certain mappings defined by S. Under an asymptotic compactness hypothesis it is proved that L is nonempty, compact and if M is connected, L
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Numerical evidence of Kneser solutions and convergence of collocation applied to singular ODEs
2015In the first chapter of the work, we give numerical evidence of Kneser solutions for second order ordinary differential equations with a singularity of the first kind on a semi infinite intervall. The main goal is to illustrate the existence theory of Kneser solutions and their asymptotic behavior In the second part of the work, we test the convergence
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Strengthening of the kneser theorem on zeros of the solutions of the equation $$y'' + p(x)y = 0$$
Ukrainian Mathematical Journal, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalization of the Kneser theorem on zeros of solutions of the equation y″ + p(t)y = 0
Ukrainian Mathematical Journal, 2007We establish conditions for the oscillation of solutions of the equation y″ + p(t)Ay = 0 in a Banach space, where A is a bounded linear operator and p: ℝ+ → ℝ+ is a continuous function.
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Ukrainian Mathematical Journal, 2011
We present conditions under which a linear homogeneous second-order equation is nonoscillatory on a semiaxis and conditions under which its solutions have infinitely many zeros.
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We present conditions under which a linear homogeneous second-order equation is nonoscillatory on a semiaxis and conditions under which its solutions have infinitely many zeros.
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On Kneser solutions of nonlinear ordinary differential equations
Doklady Mathematics, 2013openaire +1 more source