On uniformly continuous operators and some weight-hyperbolic function Banach algebra.

Barrenechea, Ana L.; Peña, Carlos C.

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Singular Dirichlet boundary value problems. II: Resonance case

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Existence results are established for the resonant problem $y^{''} + λ_{m} a y = f (t, y)$ a.e. on $[0, 1]$ with $y$ satisfying Dirichlet boundary conditions. The problem is singular since $f$ is a Carathéodory function, $a \in L_{l o c}^{1} (0, 1)$ with $a > 0$ a.e. on $[0, 1]$ and $\int_{0}^{1} x (1 - x) a (x) d x < \infty$ .

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Ryotaro Sato (2011)

Commentationes Mathematicae Universitatis Carolinae

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Yong, Jiongmin (2004)

Journal of Applied Mathematics and Stochastic Analysis

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