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Three positive solutions for second-order Neumann boundary value problems. (English) Zbl 1061.34014

Summary: Existence criteria for three positive solutions to the second-order Neumann boundary value problems \[ -u''+Mu=f(t,u),\quad u'(0)=u'(t)=0, \] and \[ u''+Mu=f(t,u),\quad u'(0)=u'(t)=0, \] are established by using the Leggett-Williams fixed-point theorem. An example is also included to illustrate the importance of the result obtained.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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