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Remarks on the existence of solutions of $x''+x+\arctan(x')=p(t)$; $x(0)=x(\pi)=0$. (English) Zbl 0802.34021
Of concern is the boundary value problem listed in the title of the paper, where $p$ is a continuous given function. The authors use the contraction mapping principle to prove an existence and uniqueness result when $\Vert p\Vert\sb \infty$ is sufficiently small. Other conditions and approaches for existence are also discussed.

34B15Nonlinear boundary value problems for ODE
34C25Periodic solutions of ODE
Full Text: DOI
[1] Kannan, R.; Ortega, R.: Existence of solutions of x” + $x + g(x) = p(t), x(0) = 0$ = x({$\pi$}). Proc. am. Math. soc. 96, 67-70 (1986) · Zbl 0585.34001
[2] Cesari, L.: Functional analysis, nonlinear differential equations and the alternative method. Nonlinear functional analysis and differential equations, 1-197 (1976) · Zbl 0343.47038
[3] Nagle, K.: Nonlinear boundary value problems for ordinary differential equations with a small parameter. SIAM J. Math. analysis 9, 719-729 (1978) · Zbl 0389.34017