Wenming Zou's Critical Point Theory and Its Applications PDF

By Wenming Zou

ISBN-10: 038732965X

ISBN-13: 9780387329659

This publication provides the various most recent examine in severe element conception, describing tools and proposing the latest purposes. insurance contains extrema, even valued functionals, vulnerable and double linking, signal altering recommendations, Morse inequalities, and cohomology teams. purposes defined contain Hamiltonian structures, Schrödinger equations and structures, leaping nonlinearities, elliptic equations and platforms, superlinear difficulties and beam equations.

Show description

Read or Download Critical Point Theory and Its Applications PDF

Similar functional analysis books

Get The Bartle-Dunford-Schwartz integral: integration with PDF

This quantity is an intensive and complete treatise on vector measures. The capabilities to be built-in should be both [0,infinity]- or genuine- or complex-valued and the vector degree can take its values in arbitrary in the neighborhood convex Hausdorff areas. additionally, the area of the vector degree doesn't must be a sigma-algebra: it will possibly even be a delta-ring.

Complex variables by Stephen D. Fisher PDF

1000s of solved examples, routines, and purposes support scholars achieve an organization realizing of an important issues within the conception and purposes of advanced variables. subject matters comprise the complicated airplane, easy homes of analytic services, analytic capabilities as mappings, analytic and harmonic services in functions, and rework equipment.

Bounded analytic functions by John Garnett PDF

This e-book is an account of the speculation of Hardy areas in a single size, with emphasis on the various fascinating advancements of the prior twenty years or so. The final seven of the 10 chapters are committed generally to those contemporary advancements. The motif of the speculation of Hardy areas is the interaction among actual, advanced, and summary research.

Download e-book for kindle: The Symmetry Perspective: From Equilibrium to Chaos in Phase by Martin Golubitsky

Trend formation in actual structures is without doubt one of the significant study frontiers of arithmetic. A relevant subject matter of this ebook is that many cases of development formation should be understood inside a unmarried framework: symmetry. The booklet applies symmetry how to more and more complicated forms of dynamic habit: equilibria, period-doubling, time-periodic states, homoclinic and heteroclinic orbits, and chaos.

Additional resources for Critical Point Theory and Its Applications

Sample text

This open problem was studied in T. Bartsch-M. Willem [48]. 7 is an improvement and generalization of the results in [48]. Another example is f{x,u) =i^|i^|^~^ln(2 + |i^|), a G (1,2); g{x,u) =/ii^ln(l + |i^|). Then (Di), (D2), (D3) and (D4)-(2) hold if /i < 0; (Di), (D2), (D3) and (D4)-(3) hold with o^ = 2 if /i > 0. If we choose g{x,u) = u'^ for |i^| < 1; g{x,u) = c|^|-i/2ln(l + 1^1) for |^| > 1, then (Di), (D2), (D3) and (D4)-(l) hold. 7. Assume that (DiJ-fD^) hold. Then equation (D) has infinitely many solutions {uk] satisfying ^{uk) '•=-\\uk\\^ — I F{x,Uk)dx — I G{x,Uk)dx ^ 0~ 2 JQ JQ as k ^ 00, where \\u\\ = (J^ | y i^p(ix)^/^.

1) {I\u^v)-I\u^w),v-w) > \\v - w\\h{\\v - w\\) for all u G Ei^v^w G ^2, then we have the following results. (1) There exists a continuous function (j) : Ei ^ E2 such that I{u -\- (j){u)) = min I{u + v). veE2 Moreover, (j){u) is the unique member of E2 such that {I'{u^(j){u)),v) =0, \JveE2. veEi. (3) An element u e Ei is a critical point of J if and only if u -\- (j){u) is a critical point of L Proof. (1) For each u G ^ 1 , define H^ : E2 ^ K by Hu{v) = I{u + v). 1), Hu is of C^ and has at most one critical point.

Li-Z. Q. Wang [217], sign-changing small energy solutions were obtained. 7 of the present chapter were obtained by W. Zou in [385]. Chapter 4 Linking and Homoclinic Type Solutions In this chapter, we first prove a weak finking tfieorem wfiicfi, to some extent, unifies the classical linking theorems. Moreover, it produces a bounded Palais-Smale sequence for a non-even functional. Applications will be given on the existence of homoclinic orbits for Hamiltonian systems and solutions to Schrodinger equations.

Download PDF sample

Critical Point Theory and Its Applications by Wenming Zou


by Charles
4.3

Rated 4.78 of 5 – based on 36 votes