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On the singular generalized Fisher-like equation with derivative depending nonlinearity. (English) Zbl 1183.34039
The existence and multiplicity of positive solutions for the second-order nonlinear boundary value problem
\[ -y'' + cy' + \lambda y= m(x) f(x,y(x),y'(x)), \quad x\in (0,+\infty), \]
\[ y(0)=y_0, \;y(+\infty)=0 \] is investigated, where \(c,\lambda\) are positive parameters, \(m\) and \(f\) are continuous functions. The term \(m\) may exhibit a singularity at the origin, while \(f\) is assumed to have a polynomial growth. Some examples and numerical computations are also presented. In order to obtain a priori estimates of the solutions, which can be non-monotone, recent fixed-point theorems on cones of Banach spaces are used.

MSC:
34B40 Boundary value problems on infinite intervals for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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