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Boundary value problems for second order nonlinear ordinary differential equations. (English) Zbl 1085.34514

Summary: The authors consider the second-order ordinary differential equation \[ u''+\lambda a(t)f(u)=0,\quad 0<t<1,\tag{E} \] with the boundary conditions \[ u(0)=u(1)=0 \tag{\(\text{B}_1\)} \] or \[ u(0)=u'(1)=0. \tag{\(\text{B}_2\)} \] Some new existence results for problems (E)–(\(\text{B}_1\)) and (E)–\((\text{B}_2\)) are obtained. Examples illustrating the results and demonstrating the sharpness of the hypotheses are included.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
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