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during the analysis of a problem in my phd thesis

I have resulted in the following equation.

[tex]\varphi(x)= \int_a^b K(x,t)\varphi(t)dt[/tex]

which is clearly ahomogeneous Fredholm equation of the second kind

The problem is that I can't find in any text any way of solving it.

Solutions are provided only for special cases like when the kernel K

is symmetric

[tex]K(x,t)=K(x,t)[/tex]

or when it is separable which are both not my case.

The particular form of the equation I am dealing with is

[tex]\varphi(x)= \int_a^b \Lambda(x,t)g(x)\varphi(t)dt[/tex]

where [tex]\Lambda(x,t)[/tex] is symmetric and g(x) a known function involving logarithm.

Any ideas of how to deal with this kind of form?

Thank you in advance

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# Homogeneous Fredholm equation of the second kind

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