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Critical Point Theory and Its Applications - download pdf or read online

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By Wenming Zou

ISBN-10: 038732965X

ISBN-13: 9780387329659

ISBN-10: 0387329684

ISBN-13: 9780387329680

This e-book provides a number of the newest study in severe element thought, describing equipment and providing the most recent functions. insurance contains extrema, even valued functionals, vulnerable and double linking, signal altering ideas, Morse inequalities, and cohomology teams. functions defined contain Hamiltonian structures, Schrödinger equations and platforms, leaping nonlinearities, elliptic equations and structures, superlinear difficulties and beam equations.

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Example text

Willem in [48] (see also T. Bartsch-M. Willem [49, 50] and M. Willem [377] ) respectively, where the (PS) condition and its variants play an important role for those abstract results and their applications. They are effective tools in studying the existence of infinitely many large or small energy solutions. Another important result on even functionals is the symmetric mountain pass theorem by taking advantage of the index theory and the (PS) condition (cf. A. Ambrosetti-P. Rabinowitz [19] and M.

Zou in [385]. 2, a " monotonicity method" is applied which was introduced by M. Struwe in [351, 352] for minimization problems and essentially developed by L. Jeanjean in [191, 193, 196] for one positive solution of mountain pass type. The readers may consult the papers of B. Buffoni-L. A. Stuart [74], D. G. de Figueiredo-P. L. Lions [163], L. Jeanjean [194], N. Hirano-S. Li-Z. Q. Wang [185], Z. Liu-S. Li-Z. Q. Wang [236], P. L. Lions [227], M. Schechter [316], M. Struwe [349] and other papers for results without the (PS) condition.

There are many examples. E x a m p l e 4 . 1 . },po = 0 G Q. For any u = u~ Qu^ e E, define F : E ^ N by Fu := u~^ then A := dQ^B := F~^{po) = E^ satisfy the above conditions. E x a m p l e 4 . 2 . Let E = E' ® E+, z^ G E+ with \\ZQ\\ = 1 , ^ + = R Z Q © E^. For any u ^ E, we write u = u~ ® sz^ © w^ with u~ G E~,s G Il,w~^ G (E-^Kzo)^ =Ef. LetN := E'^HZQ. },po = 50^0 ^ Q, So > 0. Let F : E ^ N be defined by Fu := i^~ + ||5Zo+t^^||^o, then F , (3,po satisfy the above conditions with B = F~^{soZo) = {u : = szo^w^ : s> 0,w^ G E^, \\szo ^w^\\ = so}.

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Critical Point Theory and Its Applications by Wenming Zou


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