The existence of multiple positive solutions of p-Laplacian boundary value problems
Keyword(s):
AbstractIn this paper, we establish sufficient conditions to guarantee the existence of at least three or 2n − 1 positive solutions of nonlocal boundary value problems consisting of the second-order differential equation with p-Laplacian (1) $$[\phi _p (x'(t))]' + f(t,x(t)) = 0, t \in (0,1),$$ and one of following boundary conditions (2) $$x(0) = \int\limits_0^1 {x(s) dh(s),} \phi _p (x'(1)) = \int\limits_0^1 {\phi _p (x'(s)) dg(s)} ,$$ and (3) $$\phi _p (x'(0)) = \int\limits_0^1 {\phi _p (x'(s)) dh(s),} x(1) = \int\limits_0^1 {x(s) dg(s)} .$$ Examples are presented to illustrate the main results.
2007 ◽
Vol 330
(2)
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pp. 900-915
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2003 ◽
Vol 2003
(18)
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pp. 1047-1060
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2015 ◽
Vol 23
(2)
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pp. 279-304
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Multiple positive solutions for singular nth-order nonlocal boundary value problems in Banach spaces
2011 ◽
Vol 61
(7)
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pp. 1880-1890
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