Ok I tried to solve it but obviously somewhere I have done a mistake.
First we need to find Green's function for the above problem.
Integration by parts:
$$...
I had made a post in the past about the same problem and unfortunately I wasn't clear enough
so I am trying again.
I am studying an article and there I found without any proof that the solution of:
Let ##g \in \mathbb{C}## and let ##u:(0,\infty)\to \mathbb{C}##
$$ -u''+\lambda^2u=f\,\, on...
-u''(z)+α2u(z)=f(z), u(0)=g(z), u(z)=0 as z→∞
-u''(z)+α2u'(z)=f(z), u(0)=g(z), u(z)=0 as z→∞
I am interested to solve these two boundary problems using Green's functions. It is noticed that z is complex variable. Can someone help me to do this?