科研之友
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摘要
In this paper, we consider the multipoint boundary value problem for one-dimensional p-Laplacian
(phi(p)(u'))' + q(t)f(t, u) = 0, t is an element of (0, 1),
subject to the boundary value conditions:
u(0) = (n)Sigma(i=1)alpha(i)u(xi(i)), u(1) = (n)Sigma(i=1)beta(i)u(xi(i)),
where phi(p)(s) = vertical bar S vertical bar(p-2)s, P > 1, xi(i) is an element of (0, 1) With 0 < xi(1) < xi(2) < ... < xi(n) < 1 and alpha(i),beta(i) is an element of [0, infinity) satisfy 0 < Sigma(n)(i=1) alpha(i), Sigma(n)(i=1) beta(i) < 1 The nonlinear term f may change sign. Using a fixed point theorem for operators in a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem.
