Multiple solutions of a generalized singular perturbed brate problem
article
nonlinear two-point boundary value problems (BVPs) may have none or more than one solution. For the singulary perturbed two-point BVP EU" +2u'+f(u)= 0,0 < x <1,u (0)= 0,u (1) = 0,a condition is given to have one and only one solution; also cases of more solutions have been analyzed. After attention to the form and validity of the corresponding asymptotic expansions, partially based on slow manifold theory, we reconsider the BVP within the framework of small and large values of the parameter. In the case of a special nonlinearity, numerical bifurcation patterns are studied that improve our understanding of the multivaluedness of the solutions.
Topics
Trafficasymptotic expansionsBoundary value problemsbranch pointsnumerical continuationAsymptotic analysisPerturbation techniquesAsymptotic expansionBifurcation patternsBranch pointsMultiple solutionsNumerical continuationSingularly perturbedSlow manifoldsTwo point boundary value problemsBoundary value problems
TNO Identifier
463822
ISSN
02181274
Source
International Journal orf Bifurcation and Chaos, 22(September), pp. 1250095-1-1250095-10.
Article nr.
1250095
Pages
1250095-1-1250095-10
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