- 338

- 0

## Main Question or Discussion Point

I have a BVP of the form u" + f(x)u = g(x) , u(0)=u(1)= 0

where f(x) and g(x) are positive functions.

I suspect that u(x) < 0 in the domain 0 < x < 1. How do I go proving this.

I have try proving by contradiction. Assuming first u > 0 but I can't deduce that u" > 0 which contradict that u has a maximum in the domain. Or because my conjecture is wrong

where f(x) and g(x) are positive functions.

I suspect that u(x) < 0 in the domain 0 < x < 1. How do I go proving this.

I have try proving by contradiction. Assuming first u > 0 but I can't deduce that u" > 0 which contradict that u has a maximum in the domain. Or because my conjecture is wrong