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A remark on the existence of small solutions to a fourth order boundary value problem with large nonlinearity. (English) Zbl 0779.34022
The existence of at least one small solution to the nonlinear boundary value problem \(y^{(4)}+(m^ 2+n^ 2)y''+m^ 2 n^ 2 y+\eta y^{2l}=f\), \(y^{(i)}(0)=y^{(i)}(2\pi)\), \(i=0,1,2,3\), where \(0<m<n\), \(l\geq 4\), \(m,n\in N\), \(\eta=\pm 1\), under certain assumptions on \(f\), is proved.
34B15 Nonlinear boundary value problems for ordinary differential equations
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