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A note on rapid convergence of approximate solutions for second order periodic boundary value problems

Rahmat A. Khan, Bashir Ahmad (2005)

Archivum Mathematicum

In this paper, we develop a generalized quasilinearization technique for a nonlinear second order periodic boundary value problem and obtain a sequence of approximate solutions converging uniformly and quadratically to a solution of the problem. Then we improve the convergence of the sequence of approximate solutions by establishing the convergence of order k ( ...

A note on solutions of semilinear equations at resonance in a cone

Bogdan Przeradzki (1993)

Annales Polonici Mathematici

A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).

A Note on the Divergence-Free Jacobian Conjecture in ℝ²

M. Sabatini (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We give a shorter proof to a recent result by Neuberger [Rocky Mountain J. Math. 36 (2006)], in the real case. Our result is essentially an application of the global asymptotic stability Jacobian Conjecture. We also extend some of the results of Neuberger's paper.

A note on the oscillation of second order differential equations

Hishyar Kh. Abdullah (2004)

Czechoslovak Mathematical Journal

We give a sufficient condition for the oscillation of linear homogeneous second order differential equation y ' ' + p ( x ) y ' + q ( x ) y = 0 , where p ( x ) , q ( x ) C [ α , ) and α is positive real number.

A note on the oscillation problems for differential equations with p ( t ) -Laplacian

Kōdai Fujimoto (2023)

Archivum Mathematicum

This paper deals with the oscillation problems on the nonlinear differential equation ( a ( t ) | x ' | p ( t ) - 2 x ' ) ' + b ( t ) | x | λ - 2 x = 0 involving p ( t ) -Laplacian. Sufficient conditions are given under which all proper solutions are oscillatory. In addition, we give a-priori estimates for nonoscillatory solutions and propose an open problem.

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