| preface . 1 introduction 1.1 basic ideas of variational methods 1.2 classical solution and generalized solution 1.3 first variation, euler-lagrange equation 1.4 second variation 1.5 systems 2 sobolev spaces 2.1 hslder spaces 2.2 lp spaces 2.3 sobolev spaces 3 calculus in banach spaces 3.1 frechet-derivatives 3.2 nemyski operator 3.3 gateaux-derivatives 3.4 calculus of abstract functions 3.5 initial value problem in banach space 4 direct methods 4.1 lower semi-continuity 4.2 a general lower semi-continuity result .4.3 ekeland variational principle 4.4 palais-smale condition 4.5 constrained variational problems 5 deformation theorems .. 5.1 deformations in hilbert space 5.2 pseudo-gradient vector field 5.3 deformations in banach space 6 minimax methods 6.1 general minimax principle 6.2 mountain pass lemma 6.3 z2 index theory 6.4 linking argument 6.5 p-laplacian with indefinite weights 7 noncompact variational problems 7.1 poh0zaev type identities 7.2 symmetry and compactness 7.3 concentration compactness principles 7.4 unconstrained problems involving critical sobolev exponent 8 generalized k-p equation 8.1 solitary waves 8.2 stationary solutions to gkp equation in bounded domain 9 best constants in sobolev inequalities 9.1 best constants 9.2 applications 9.3 extensions appendix a elliptic regularity a.1 local boundedness a.2 hslder continuity bibliography index ... |
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