I have a problem with this first order DE: let $-\infty and
$u'(x)+(\lambda+q(x))u(x)=0,\tag{1}$ where $u$ is a continuous and real valued, while $\lambda$ is a parameter not depending on $x$.
A strange non trivial boundary condition is given, namely $\alpha u(a)+\alpha'u'(a)+\beta u(b)+\beta'u'(b)=0.$
Then I have to show that this problem admits at most three eigenvalues.
What I have tried: basically to convert this problem into a Sturm Liouville problem, however I couldn't conclude anything.
Can anybody help me?
How to go through this kind of problems? thanks in advance.
-Guido-