| Abstract: |
| In this talk I will consider a perturbed Hammerstein integral equation of the form
\begin{equation}
y(t)=\gamma_1(t)H_1\big(\varphi_1(y)\big)+\gamma_2(t)H_2\big(\varphi_2(y)\big)+\lambda\int_0^1G(t,s)f\big(s,y(s)\big)\ ds.\notag
\end{equation}
Since $\varphi_1$ and $\varphi_2$ are linear functionals, solutions of this type of integral equation can be related to solutions of nonlocal boundary value problems. I will show that by introducing a nonstandard order cone one can equip the linear functionals with coercivity conditions that are useful for the improvement of existence results for both the integral equation and associated boundary value problems for ODEs and elliptic PDEs on annuli. |
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