| Abstract: |
| The talk concerns some recent results about third-order strongly nonlinear differential equations of the type
\[ (\Phi(k(t)u``(t)))` = f(t,u(t),u`(t),u``(t)), \ \ \text{ a.e. on } [0,T] \]
where \(\Phi\) is a strictly increasing homeomorphism and the nonnegative function \(k\) may vanish on a set of measure zero.
By using the upper and lower solutions method, existence results for boundary value problems, associated to the above equation, are proved.
Moreover, second-order integro-differential equations of the type
\[ (\Phi(k(t)v`(t)))` = f(t,\int_0^t v(\tau)\ d \tau, \ v(t),\ v`(t)), \ \ \text{ a.e. on } [0,T] \]
are also considered, for which existence results for various types of boundary conditions, including periodic, Sturm-Liouville and Neumann-type conditions, are provided. |
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