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A class of nonlinear boundary value problems in Banach spaces. (Chinese. English summary) Zbl 0832.34056

Summary: We consider boundary value problems in Banach spaces of the form \(\ddot x= f(t, x, \dot x)\) \((0\leq t\leq 1)\), \(\alpha_i x(i)+ \beta_i\dot x(i)= \xi_i\) \((i= 0,1)\). By means of the concept of the so-called \(\gamma\)-Lipschitz modulus of a map, we obtain some existence theorems for such a boundary value problem.

MSC:

34G20 Nonlinear differential equations in abstract spaces
34B15 Nonlinear boundary value problems for ordinary differential equations
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