1 Constrained minimization -- 1.1 Preliminaries -- 1.2 Constrained minimization -- 1.3 Dual method -- 1.4 Minimizers with the least energy -- 1.5 Application of dual method -- 1.6 Multiple solutions of nonhomogeneous equation -- 1.7 Sets of constraints -- 1.8 Constrained minimization for Ff -- 1.9 Subcritical problem -- 1.10 Application to the p-Laplacian -- 1.11 Critical problem -- 1.12 Bibliographical notes -- 2 Applications of Lusternik-Schnirelman theory -- 2.1 Palais-Smale condition, case ρ ≠ q -- 2.2 Duality mapping -- 2.3 Palais-Smale condition, case ? = q -- 2.4 The Lusternik-Schnirelman theory -- 2.5 Case ρ > q -- 2.6 Case ρ q -- 3.8 Set of constraints V -- 3.9 Application to a critical case ρ = n -- 3.10 Technical lemmas -- 3.11 Existence result for problem (3.34) -- 3.12 Bibliographical notes -- 4 Potentials with covariance condition -- 4.1 Preliminaries and constrained minimization -- 4.2 Dual method -- 4.3 Minimization subject to constraint V -- 4.4 Sobolev inequality -- 4.5 Mountain pass theorem and constrained minimization -- 4.6 Minimization problem for a system of equations -- 4.7 Bibliographical notes -- 5 Eigenvalues and level sets -- 5.1 Level sets -- 5.2 Continuity and monotonicity of σ -- 5.3 The differentiability properties of σ -- 5.4 Schechter's version of the mountain pass theorem.

5.5 General condition for solvability of (5.11) -- 5.6 Properties of the function κ(t) -- 5.7 Hilbert space case -- 5.8 Application to elliptic equations -- 5.9 Bibliographical notes -- 6 Generalizations of the mountain pass theorem -- 6.1 Version of a deformation lemma -- 6.2 Mountain pass alternative -- 6.3 Consequences of mountain pass alternative -- 6.4 Hampwile alternative -- 6.5 Applicability of the mountain pass theorem -- 6.6 Mountain pass and Hampwile alternative -- 6.7 Bibliographical notes -- 7 Nondifferentiable functionals -- 7.1 Concept of a generalized gradient -- 7.2 Generalized gradients in function spaces -- 7.3 Mountain pass theorem for locally Lipschitz functionals -- 7.4 Consequences of Theorem 7.3.1 -- 7.5 Application to boundary value problem with discontinuous nonlinearity -- 7.6 Lower semicontinuous perturbation -- 7.7 Deformation lemma for functionals satisfying condition (L) -- 7.8 Application to variational inequalities -- 7.9 Bibliographical notes -- 8 Concentration-compactness principle - subcritical case -- 8.1 Concentration-compactness principle at infinity - subcritical case -- 8.2 Constrained minimization - subcritical case -- 8.3 Constrained minimization with b ≢ φ const, subcritical case -- 8.4 Behaviour of the Palais-Smale sequences -- 8.5 The exterior Dirichlet problem -- 8.6 The Palais-Smale condition -- 8.7 Concentration-compactness principle I -- 8.8 Bibliographical notes -- 9 Concentration-compactness principle - critical case -- 9.1 Critical Sobolev exponent -- 9.2 Concentration-compactness principle II -- 9.3 Loss of mass at infinity -- 9.4 Constrained minimization - critical case -- 9.5 Palais-Smale sequences in critical case -- 9.6 Symmetric solutions -- 9.7 Remarks on compact embeddings into L2*(Q) and L2*K (R)n -- 9.8 Bibliographical notes -- Appendix -- A.1 Sobolev spaces -- A.2 Embedding theorems.

A.3 Compact embeddings of spaces W1,p(Rn) and D1,p(Rn) -- A.4 Conditions of concentration and uniform decay at infinity -- A.5 Compact embedding for H1R (Rn) -- A.6 Schwarz symmetrization -- A.7 Pointwise convergence -- A.8 Gâteaux derivatives -- Bibliography -- Glossary -- Index.