Nonlinear boundary value problems in Hilbert spaces.(English)Zbl 0672.34056

The authors consider the nonlinear two point boundary value problem (*) $$y''=f(t,y,y')$$, $$0\leq t\leq 1$$, with Sturm-Liouville type boundary conditions. A solution of (*) is a twice continuously differentiable function which takes values in a real Hilbert space H. The nonlinear term f ([0,1]$$\times H\times H\to H)$$ is always assumed to be continuous. Subject to various restrictions on f, including a Bernstein-Nagumo type growth condition, the authors prove certain existence theorems for a wide class of problems.
Reviewer: K.S.Miller

MSC:

 34G20 Nonlinear differential equations in abstract spaces 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations
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References:

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