Asymptotics of Nonlinearities and Operator Equations

Foreword.- 1: Norm estimates for solutions of integral-functional inequalities.- §1. Distribution functions.- §2. Estimates for solutions of the basic integral-functional inequality.- §3. Proof of Theorem 2.2.- §4. A second integral-functional inequality.- §5. Proofs of Theorems 4.1-4.4.- §6. Additional remarks.- 2: Two-sided estimates for nonlinearities.- §7. Equations with self-adjoint and normal operators.- §8. Solvability of equations in case the solutions do not admit a priori norm estimates.- §9. Proofs of Theorems 8.1 and 8.2.- §10. Two-point boundary value problems.- §11. Forced oscillations in control systems.- 3: The use of arguments of leading eigenvalues.- §12. Use of the arguments principle.- §13. Joint norms of operators.- §14. Two-point boundary value problems (the nonquasilinear case).- §15. Forced oscillations in quasilinear systems.- §16. Forced oscillations in systems with delay.- §17. Remarks on forced oscillations in systems with control by derivatives.- §18. Extensions of the joint norm method.- 4: Weak nonlinear it ies.- §19. Equations with weak nonlinearities.- §20. Equations with normal operators.- §21. Auxiliary results.- §22. Equations with nonnormal operators.- §23. Integral equations with nonnegative kernels.- §24. Landesman-Lazer type theorems.- §25. Asymptotic bifurcation points.- 5: One-sided estimates for nonlinearities.- §26. Positive linear operators.- §27. Solvability of nonlinear operator equations with positive linear part.- §28. Equations with strictly positive operators.- §29. Two-point boundary value problems (the quasilinear case).- §30. Potential positivity of the periodic problem operator.- §31. Multiply-connected control systems.- §32. One-sided estimates in nonquasilinear problems.- §33. First order equations with variable coefficients.- §34. Variational methods.- References.- List of Symbols.