Positive solutions of higher order quasilinear elliptic equations
Keyword(s):
A Priori
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The higher order quasilinear elliptic equation−Δ(Δp(Δu))=f(x,u)subject to Dirichlet boundary conditions may have unique and regular positive solution. If the domain is a ball, we obtain a priori estimate to the radial solutions via blowup. Extensions to systems and general domains are also presented. The basic ingredients are the maximum principle, Moser iterative scheme, an eigenvalue problem, a priori estimates by rescalings, sub/supersolutions, and Krasnosel'skiĭ fixed point theorem.
2006 ◽
Vol 27
(2)
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pp. 159-177
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2018 ◽
Vol 7
(4)
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pp. 425-447
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2002 ◽
Vol 7
(2)
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pp. 207-216
2002 ◽
Vol 130
(10)
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pp. 3043-3050
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