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AuthorMorokoff, William J. author
TitleAsymptotics of Nonlinearities and Operator Equations [electronic resource] / by Alexander M. Krasnosel'skii
ImprintBasel : Birkhรคuser Basel, 1995
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Descript 278 p. online resource


New methods for solving classical problems in the theory of nonlinear operator equations (solvability, multiple solutions, bifurcations, nonlinear resonance, potential methods, etc) are introduced and discussed. The general abstract theorems are illustrated by various applications to differential equations and boundary value problems. In particular, the problem on forced periodic oscillations is considered for equations arising in control theory


Foreword -- 1: Norm estimates for solutions of integral-functional inequalities -- ยง1. Distribution functions -- ยง2. Estimates for solutions of the basic integral-functional inequality -- ยง3. Proof of Theorem 2.2 -- ยง4. A second integral-functional inequality -- ยง5. Proofs of Theorems 4.1-4.4 -- ยง6. Additional remarks -- 2: Two-sided estimates for nonlinearities -- ยง7. Equations with self-adjoint and normal operators -- ยง8. Solvability of equations in case the solutions do not admit a priori norm estimates -- ยง9. Proofs of Theorems 8.1 and 8.2 -- ยง10. Two-point boundary value problems -- ยง11. Forced oscillations in control systems -- 3: The use of arguments of leading eigenvalues -- ยง12. Use of the arguments principle -- ยง13. Joint norms of operators -- ยง14. Two-point boundary value problems (the nonquasilinear case) -- ยง15. Forced oscillations in quasilinear systems -- ยง16. Forced oscillations in systems with delay -- ยง17. Remarks on forced oscillations in systems with control by derivatives -- ยง18. Extensions of the joint norm method -- 4: Weak nonlinear it ies -- ยง19. Equations with weak nonlinearities -- ยง20. Equations with normal operators -- ยง21. Auxiliary results -- ยง22. Equations with nonnormal operators -- ยง23. Integral equations with nonnegative kernels -- ยง24. Landesman-Lazer type theorems -- ยง25. Asymptotic bifurcation points -- 5: One-sided estimates for nonlinearities -- ยง26. Positive linear operators -- ยง27. Solvability of nonlinear operator equations with positive linear part -- ยง28. Equations with strictly positive operators -- ยง29. Two-point boundary value problems (the quasilinear case) -- ยง30. Potential positivity of the periodic problem operator -- ยง31. Multiply-connected control systems -- ยง32. One-sided estimates in nonquasilinear problems -- ยง33. First order equations with variable coefficients -- ยง34. Variational methods -- References -- List of Symbols

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