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Twin solutions to singular Dirichlet problems. (English) Zbl 0946.34022

The authors consider the Dirichlet second-order boundary value problem \[ y''+ \phi(t)[g(y(t))+ h(y(t))]= 0,\quad 0< t< 1,\quad y(0)= y(1)= 0,\tag{1} \] and establish the existence of two solutions \(y_1,y_2\in C[0,1]\cap C^2(0, 1)\) with \(y_1> 0\), \(y_2> 0\) on \((0,1)\). The nonlinearity in (1) may be singular at \(y= 0\), \(t= 0\) and/or \(t= 1\).

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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