000			03498cam a2200325Mi 4500
001			ocn957655684
005			20240726105029.0
008			160902s2016 xx o 000 0 eng d
040			_aIDEBK _beng _epn _erda _cIDEBK _dYDX _dNT _dOCLCF _dOCLCQ _dOCLCO _dOCLCQ _dCUY _dIGB _dAGLDB _dDEGRU _dD6H _dCN8ML _dOCLCQ _dVTS _dLVT _dS9I
020			_a9781400884339 _q((electronic)l(electronic)ctronic)
050	0	4	_aQA380 _b.A535 2016
100	1		_aBuffoni, Boris, _d1965- _e1
245	1	0	_aAnalytic Theory of Global Bifurcation.
260			_bPrinceton University Press, _c(c)2016.
300			_a1 online resource
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_adata file _2rda
490	0		_aPrinceton Series in Applied Mathematics
504			_a2
505	0	0	_aFrontmatter -- _tContents -- _tPreface -- _tChapter 1. Introduction -- _tPart 1. Linear and Nonlinear Functional Analysis -- _tChapter 2. Linear Functional Analysis -- _tChapter 3. Calculus in Banach Spaces -- _tChapter 4. Multilinear and Analytic Operators -- _tPart 2. Analytic Varieties -- _tChapter 5. Analytic Functions on F -- _tChapter 6. Polynomials -- _tChapter 7. Analytic Varieties -- _tPart 3. Bifurcation Theory -- _tChapter 8. Local Bifurcation Theory -- _tChapter 9. Global Bifurcation Theory -- _tPart IV. Stokes Waves -- _tChapter 10. Steady Periodic Water Waves -- _tChapter 11. Global Existence of Stokes Waves -- _tBibliography -- _tIndex
520	0		_aRabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are connected sets of solutions of global extent. Even when the operators are infinitely differentiable in all the variables and parameters, connectedness here cannot in general be replaced by path-connectedness. However, in the context of real-analyticity there is an alternative theory of global bifurcation due to Dancer, which offers a much stronger notion of parameter dependence. This book aims to develop from first principles Dancer's global bifurcation theory for one-parameter families of real-analytic operators in Banach spaces. It shows that there are globally defined continuous and locally real-analytic curves of solutions. In particular, in the real-analytic setting, local analysis can lead to global consequences--for example, as explained in detail here, those resulting from bifurcation from a simple eigenvalue. Included are accounts of analyticity and implicit function theorems in Banach spaces, classical results from the theory of finite-dimensional analytic varieties, and the links between these two and global existence theory. Laying the foundations for more extensive studies of real-analyticity in infinite-dimensional problems and illustrating the theory with examples, Analytic Theory of Global Bifurcation is intended for graduate students and researchers in pure and applied analysis.
530			_a2 _ub
650		0	_aBifurcation theory.
655		1	_aElectronic Books.
856	4	0	_uhttps://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1353578&site=eds-live&custid=s3260518 _zClick to access digital title | log in using your CIU ID number and my.ciu.edu password
942			_cOB _D _eEB _hQA _m2016 _QOL _R _x _8NFIC _2LOC
999			_c86579 _d86579
902			_a1 _bCynthia Snell _c1 _dCynthia Snell