Positive bounded solutions for nonlinear polyharmonic problems in the unit ball
2017 ◽
Vol 25
(3)
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pp. 143-153
Keyword(s):
Abstract In this paper, we study the existence of positive solutions for the following nonlinear polyharmonic equation (-∆)mu+λf(x, u) = 0 in B; subject to some boundary conditions, where m is a positive integer, λ is a nonnegative constant and B is the unit ball of ℝn (n ≥ 2). Under some appropriate assumptions on the nonnegative nonlinearity term f(x, u) and by using the Schäuder fixed point theorem, the existence of positive solutions is obtained. At last, examples are given for illustration.
2018 ◽
Vol 21
(3)
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pp. 716-745
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2009 ◽
Vol 35
(1-2)
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pp. 341-349
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2015 ◽
Vol 20
(2)
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pp. 188-204
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2003 ◽
Vol 46
(2)
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pp. 279-292
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