| Abstract: |
| We present existence results for semilinear non autonomous evolution equations with nonlocal initial conditions, covering both first and second-order problems. In the first-order setting, a finite-dimensional reduction combined with the Leray Schauder continuation principle yields solutions in L2, under demicontinuity and transversality assumptions on the nonlinearity. The second-order analysis relies on fundamental solution techniques and Schauder type fixedpoint arguments for wave equations. Superlinear nonlinearities are handled via maximal regularity and energy inequalities in uniformly smooth Banach spaces. Applications include vibrating membranes, population dynamics with memory effects, and parabolic problems with logistic or Nagumo type reactions. |
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