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Existence MD Estimates for Solutions of Nonlinear Equations Near a Branch Point

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Existence MD Estimates for Solutions of Nonlinear Equations Near a Branch Point

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dc.contributor.author Eisenfeld, Jerome en
dc.contributor.author Lakshmikantham, V. en
dc.date.accessioned 2010-05-26T15:35:54Z en
dc.date.available 2010-05-26T15:35:54Z en
dc.date.issued 1973-12 en
dc.identifier.uri http://hdl.handle.net/10106/2170 en
dc.description.abstract Consider the equation (1.1) [see pdf for notation] on a Hilbert space H. Here n is a scalar and [see pdf for notation] is a linear Fredholm operator. That is: (a) L is closed; (b) The domain, D(L) is dense in H; (c) The range, R(L) is closed in H; (d) The dimension of the null space, dim n(L) <= (e) The dimension of the null space of the adjoint dim n(L*) <= The operator N, which may be nonlinear, is defined for sufficiently small and appropriately restricted [see pdf for notation], and [see pdf for notation] Using the method of Lyapunov-Schmidt (cf., e.g. [4] or [5]) we express w in the form (1.2) [see pdf for notation] where [see pdf for notation] denotes the orthogonal complement of n(L) in H. Suppose (u,v) satisfy the simultaneous equations (1.3) [see pdf for notation] (1.4) [see pdf for notation] where P is the orthogonal projection operator of H onto R(L), I is the identity operator on H, and J is a right inverse of L on R(L), i.e. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;3 en
dc.subject Nonlinear equations en
dc.subject Lyapunov-Schmidt en
dc.subject Branching equation en
dc.subject.lcsh Mathematics Research en
dc.title Existence MD Estimates for Solutions of Nonlinear Equations Near a Branch Point en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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