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ArticleKorman, PhilipWe consider positive solutions of the Dirichlet problem u(x) + λf(u(x)) = 0 on (−1, 1), u(−1 ) =u(1) = 0. depending on a positive parameter λ. Each solution u(x) is an even function, and hence it is uniquely identified by α = u(0). We present a formul . . .

ArticleLi, Yi LiWe present exact multiplicity results for the boundary value problems of the type (1.1) u’’+ λf(x, u) = 0 for − L < x < L, u(−L) = u(L) = 0, with the nonlinearity f behaving like a cubic polynomial in u.

Conference paper or proceedingsKorman, PhilipWe use bifurcation theory to show the existence of infinitely many solutions at the first eigenvalue for a class of Dirichlet problems in one dimension.

ArticleKorman, PhilipFor very general twopoint boundary value problems we show that any positive solution satisfies a certain integral relation. As a consequence we obtain some new uniqueness and multiplicity results.

ArticleKorman, PhilipWe consider signchanging solutions of the Dirichlet problem u +λ f(u )= 0, 0 < x < 1, u(0 )= u(1 )= 0, with n 0 interior roots. We give a necessary and sufficient condition that a turn occurs at the solution (λ,u(x)), depending only on the maximum va . . .

Conference paper or proceedingsKorman, PhilipWe present an algorithm for computing the direction of pitchfork bifurcation for twopoint boundary value problems. The formula is rather involved, but its computational evaluation is quite feasible. As an application, we obtain a multiplicity result. . . .

ArticleKorman, PhilipWe revisit the question of exact multiplicity of positive solutions for a class of Dirichlet problems for cubiclike nonlinearities, which we studied in 161. Instead of computing the direction of bifurcation as we did in [6], we use an indirect approa . . .

ArticleLi, Yi LiFor a class of twopoint boundary value problems we prove exactness of an Sshaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like for [formula].