| Abstract: |
| In this talk we will present results of existence and localization of solutions for nonlocal differential problems in abstract spaces. In particular, we will show an approach based on the so called transversality conditions, novel in this setting. This technique provides a unifying method for studying models describing reaction-diffusion processes in several frameworks. We will consider nonlocal initial conditions such as the Cauchy multipoint and the mean value conditions, and we can handle nonlinearity with superlinear growth, for instance cubic polynomials or maps depending on the integral of the solution, thus encompassing nonlocal diffusion behaviours. |
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