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Existence of three positive solutions for some second-order boundary value problems. (English) Zbl 1066.34019

Summary: A new fixed-point theorem of functional type in a cone is established. Using this fixed-point theorem and imposing growth conditions on the nonlinearity, the existence of three positive solutions for the boundary value problem \[ x''(t)+ f(t, x(t), x'(t))= 0\quad 0< t< 1,\quad x(0)= x(1)= 0, \] is obtained. Here, \(f: [0,1]\times [0,\infty)\times\mathbb{R}\to[0,\infty)\) is continuous. Finally, an example is given to illustrate the importance of results 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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