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SOLVABILITY FOR SOME DIRICHLET PROBLEM WITH P-LAPACIAN  

Kim, Yong-In (DEPARTMENT OF MATHEMATICS, UNIVERSITY OF ULSAN)
Publication Information
The Pure and Applied Mathematics / v.17, no.3, 2010 , pp. 257-268 More about this Journal
Abstract
We investigate the existence of the following Dirichlet boundary value problem $({\mid}u = (p - 1)h(t), u(0) = u(T) = 0, where p > 1, $\alpha$ > 0, $\beta$ > 0 and ${\alpha}^{-\frac{1}{p}}\;+\;{\beta}^{-\frac{1}{p}}\;=\;2$, $T\;=\;{\pi}_p/{\alpha}^{\frac{1}{p}}$, ${\pi}_p\;=\; \frac{2{\pi}}{p\;sin(\pi/p)}$ and $h\;{\in}\;L^{\infty}$(0,T). The results of this paper generalize some early results obtained in [8] and [9]. Moreover, the method used in this paper is elementary and new.
Keywords
Dirichlet problem; p-Laplacian; Fredholm alternative;
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