Titlebook: An Introduction to Nonlinear Functional Analysis and Elliptic Problems; Antonio Ambrosetti,David Arcoya Textbook 2011 Springer Science+Bus

滑稽

Superlinear Problems,s case an appropriate approach seems to be critical point theory. Actually, the mountain pass theorem or the linking theorem can be used to find solutions. We also show how to study superlinear problems by using the topological degree.

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Quasilinear Problems,ed because the Euler functional fails to be .. This critical point result is discussed in Section 12.2 and is applied to boundary value problems in Section 12.3. A nonvariational equation is also considered in Section 12.4, where we apply the global bifurcation theorem (see Theorem 4.4.1).

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Chemie – Entdecken und verstehenIn this chapter we discuss the classical Banach contraction principle and a fixed point theorem for increasing operators that will be used in connection to suband super-solutions of elliptic boundary value problems.

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Debility

https://doi.org/10.1007/978-3-662-26032-6This chapter deals with variational methods. In addition to the existence of minima of a functional, we discuss the mountain pass theorem, and the linking theorem which are used to find saddle points. A perturbation method, variational in nature, is studied in the last section.

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Mnemonics

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Das Problem und seine Untersuchung,This chapter deals with nonlinear problems with nonlinearities whose behavior at +∞ and −∞ jumps through an eigenvalue of the linear part.

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Das Problem und seine Untersuchung,This final chapter deals with the existence of ground and bound states of nonlinear Schrödinger (NLS) equations. Semiclassical states are discussed in Sect. 13.2. Systems of coupled NLS equations are handled in Sects. 13.3 and 13.4.