On positive solutions of boundary value problems for second-order functional differential equations on infinite intervals. (English) Zbl 1036.34075

The authors study the functional boundary value problem \[ \begin{gathered} x''(t)- px'(t)- qx(t)+ f(t, x_t, x_t')= 0,\quad t\geq 0,\\ \alpha x(t)-\beta x'(t)= \xi(t),\quad -\tau\leq t\leq t0,\quad \lim_{t\to\infty}\, x(t)= 0,\end{gathered} \] with \(p,\alpha,\beta\in [0,\infty)\), \(\alpha^2+ \beta^2> 0\), \(q> 0\) and \(x_t(\theta)= x(t+ \theta)\) for \(\theta\in [-\tau, 0]\). They give conditions for the existence of positive solutions to the above problem. Existence results are proved by a fixed-point theorem on cones.


34K10 Boundary value problems for functional-differential equations
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