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Existence of three solutions for a first-order problem with nonlinear nonlocal boundary conditions. (English) Zbl 1314.34048

Summary: Conditions for the existence of at least three positive solutions to the nonlinear first-order problem with a nonlinear nonlocal boundary condition given by \[ \begin{aligned} & y'(t)-r(t)y(t)=\sum\limits_{i=1}^mf_i\biggl(t,y(t)\biggr),\quad t\in [0,1],\\ & \lambda y(0)=y(1)+\sum\limits_{j=1}^n\Lambda_j(\tau_j,y(\tau_j)),\quad \tau_j\in [0,1]\end{aligned} \] are discussed, for sufficiently large \(\lambda>1\) and \(r\geq 0\). The Leggett-Williams fixed point theorem is used.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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References:

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