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Multiple nonnegative solutions of second-order systems of boundary value problems. (English) Zbl 0973.34014
The author deals with the existence of at least two nonnegative solutions to a vector boundary value problem of the form $$x''+\lambda a(t)f(x(t),y(t))=0, \quad y''+\lambda b(t)g(x(t),y(t))=0, \quad 0\le t\le 1,$$ with the boundary conditions $x(0)=x(1)=0$ and $y(0)=y(1)=0.$ The dimensions of the range of the functions $f$ and $g$ are not necessary the same. The functions $a,b$ are diagonal-valued with positive components. The author provides sufficient conditions so that by applying a fixed-point theorem in a cone the existence of at least two nonnegative solutions is guarranteed.

34B15Nonlinear boundary value problems for ODE
Full Text: DOI
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