Nonnegative solutions of singular boundary value problems with sign changing nonlinearities
The paper presents sufficient conditions for the existence of positive solutions of the equation x"(t) + q(t)f(t, x(t), x'(t)) = 0 with the Dirichlet conditions x(0) = 0, x(1) = 0 and of the equation (p(t)x'(t))' + p(t)q(t)f(t, x(t), p(t)x'(t)) = 0 with the boundary conditions lim(t-->0+) p(t)x'(t) = 0, x(1) = 0. Our nonlinearity f is allowed to change sign and f may be singular at x = 0. The proofs are based on a combination of the regularity and sequential techniques and the method of lower and upper functions. (C) 2003 Elsevier Ltd. All rights reserved.
sign changing nonlinearity positive solution singular dirichlet problem singular mixed problem