科研之友
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摘要
We treat the nonhomogeneous boundary value problems with phi-Laplacian operator (phi(u'(t)))' = -f (t, u(t), u'(t)), t. (0, T), u(0) = A, f(u'(T)) = t u(T)+ Sigma(k)(i=1) tau(i)u(zeta(i)), where phi : (-a, a) -> (-b, b) (0 < a, b <= + infinity) is an increasing homeomorphism such that phi(0) = 0, tau, tau(i) is an element of R, zeta(i) is an element of (O, T), i = 1,2,..., k, A >= 0, and f : [O, T] x R x R. R is continuous. We will show that even if some of the t and ti are negative, the boundary value problem with singular f-Laplacian operator is always solvable, and the problem with a bounded f-Laplacian operator has at least one positive solution.
