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The existence of multiple positive solutions of $p$-Laplacian boundary value problems

In: Mathematica Slovaca, vol. 57, no. 3
Yuji Liu

Details:

Year, pages: 2007, 225 - 242
About article:
In 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

$$ [φp(x'(t))]'+f(t,x(t))=0,    t\in (0,1), \eqno{(1)} $$

and one of following boundary conditions

$$ x(0)=\int01x(s) \mathrm{d}h(s),   φp(x'(1))=\int01φp(x'(s)) \mathrm{d} g(s), \eqno{(2)} $$

and

$$ φp(x'(0))=\int01φp(x'(s)) \mathrm{d} h(s),   x(1)=\int01x(s) \mathrm{d} g(s). \eqno{(3)} $$

Examples are presented to illustrate the main results.
How to cite:
ISO 690:
Liu, Y. 2007. The existence of multiple positive solutions of $p$-Laplacian boundary value problems. In Mathematica Slovaca, vol. 57, no.3, pp. 225-242. 0139-9918.

APA:
Liu, Y. (2007). The existence of multiple positive solutions of $p$-Laplacian boundary value problems. Mathematica Slovaca, 57(3), 225-242. 0139-9918.