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Multiple unbounded positive solutions for three-point BVPs with sign-changing nonlinearities on the positive half-line. (English) Zbl 1195.34042

The authors consider the following second-order nonlinear three-point boundary value problem on the positive half-line

-x '' +cx ' +λx=f(t,x(t),x ' (t)),t(0,),
x(0)-αx(η)=a 0 ,lim t x ' (t) re rt =b 0 ,

where a 0 ,b 0 are nonnegative real numbers, α0, η>0, c,λ are real positive constants, r(0,c), and f:(0,)×[0,)× is a Carathéodory function which may change sign. Under general polynomial growth conditions on f the existence of nontrivial single and multiple unbounded positive solutions is proved via fixed point theorems in a cone in a special weighted Banach space.

34B40Boundary value problems for ODE on infinite intervals
34B15Nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
34B16Singular nonlinear boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
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