Sixth Mississippi State Conference on Differential Equations and
Computational Simulations.
Electron. J. Diff. Eqns., Conference 15 (2007), pp. 239249.
On the exact multiplicity of solutions for boundaryvalue
problems via computing the direction of bifurcations
Joaquin Rivera, Yi Li
Abstract:
We consider positive solutions of the Dirichlet problem
depending on a positive parameter
.
We use two formulas derived in
[18] to compute all solutions
where a turn may occur and to
compute the direction of the turn. As an application, we consider quintic a
polynomial
with positive and distinct roots. For such quintic
polynomials we conjecture the exact mutiplicity structure of positive
solutions and present computer assisted proofs of such exact bifurcation
diagrams for various distributions of the real roots. The limiting behavior
of the solutions on these bifurcation branches as
and
their stabilities are also investigated.
Published February 28, 2007.
Math Subject Classifications: 34B15.
Key Words: Bifurcation points; direction of the turn; multiplicity of solutions.
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Joaquin Rivera
Department of Mathematics,
University of Iowa
Iowa City, Iowa 52242, USA
email: rvera@math.uiowa.edu 

Yi Li
Department of Mathematics,
University of Iowa
Iowa City, Iowa 52242, USA.
Hunan Normal University
Changsha 410081, Hunan, China
email: yili@uiowa.edu 
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