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Existence of nondensely defined evolution equations with nonlocal conditions. (English) Zbl 1170.34345
The author studies the existence of integral solutions for some evolution equations in Banach spaces with nonlocal conditions. The linear part is not necessarily densely defined and satisfies the Hille-Yosida condition, which means that it is the generator of an integrated semigroup. The nonlocal function is assumed to be lipschitzian. The author uses a fixed point argument to prove the main result of the paper. Some application are provided for illustration.
MSC:
34G20Nonlinear ODE in abstract spaces
47D06One-parameter semigroups and linear evolution equations
47N20Applications of operator theory to differential and integral equations