Marino, Giuseppe; Pietramala, Paolamaria Boundary value problems with nonlinear boundary conditions in Banach spaces. (English) Zbl 0722.34058 Commentat. Math. Univ. Carol. 31, No. 4, 711-721 (1990). The existence of a solution of \(x'=A(t,x)x+f(t,x)\) which satisfies the condition \(Lx=H(x)\) is proved where X is a Banach space, \(J=[a,b]\), A(t,x) is a bounded operator defined and continuous on \(J\times X\), f(t,x) is a continuous function on \(J\times X\), L: C(J,X)\(\to X\) is a bounded linear operator and H: C(J,X)\(\to X\) is a continuous operator not necessarily linear. The proof is based on Schaefer’s fixed point theorem. Reviewer: W.Šeda (Bratislava) Cited in 2 Documents MSC: 34K10 Boundary value problems for functional-differential equations 34K30 Functional-differential equations in abstract spaces 34B15 Nonlinear boundary value problems for ordinary differential equations 34G20 Nonlinear differential equations in abstract spaces Keywords:evolution operator; boundary value problem; nonlinear operator; existence of a solution; Banach space; Schaefer’s fixed point theorem PDFBibTeX XMLCite \textit{G. Marino} and \textit{P. Pietramala}, Commentat. Math. Univ. Carol. 31, No. 4, 711--721 (1990; Zbl 0722.34058) Full Text: EuDML