Abstract
Let α > 0 and let μ be a bounded Radon measure on the interval (-1, 1). We are interested in the equation -(|x|2αu′)′ + u = μ on (-1, 1) with boundary condition u(-1) = u(1) = 0. We identify an appropriate concept of solution for this equation, and we establish some existence and uniqueness results. The cases 0 < α < 1 and α ≥ 1 must be considered separately. We also study the limiting behavior of two different approximation schemes: one is the elliptic regularization and the other is to approximate a measure μ by a sequence of L∞-functions.
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