| 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 some techniques that weaken the classical compactness hypotheses often present in the literature for the study of this type of problems with topological methods. Furthermore, through the use of Lyapunov functions, we can consider very general growth conditions on the nonlinear term. This approach 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 of integral type which accounts for nonlocal diffusion behaviors. |
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