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The Existence and Multiplicity of Solutions of Wave Equations

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Index theory in nonlinear analysis
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Abstract

In this chapter, we apply the index theories defined in Chap. 3 to study the existence and multiplicity of solutions of wave equations. We will use the same concepts and notations as in Sect. 3.3.

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References

  1. Amann, H.: Saddle points and multiple solutions of differential equations. Math. Z. 169, 122–166 (1979)

    Article  MathSciNet  Google Scholar 

  2. Chang, K.: Infinite Dimensional Morse Theory and Multiple Solution Problems. Birkhäuser, Basel (1993)

    Book  Google Scholar 

  3. Coron, J.: Periodic solutions of a nonlinear wave equation without assumption of monotonicity. Math. Ann. 262, 273–285 (1983)

    Article  MathSciNet  Google Scholar 

  4. Dong, Y.: Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations. Calc. Var. 38, 75–109 (2010)

    Article  MathSciNet  Google Scholar 

  5. Ekeland, I.: Convexity Methods in Hamiltonian Mechanics. Springer, Berlin (1990)

    Book  Google Scholar 

  6. Ghoussoub, N.: Duality and Perturbation Methods in Critical Point Theory. Cambridge University Press, Cambridge (1993)

    Book  Google Scholar 

  7. Liu, Z., Su, J., Wang, Z.: A twist condition and periodic solutions of Hamiltonian system. Adv. Math. 218, 1895–1913 (2008)

    Article  MathSciNet  Google Scholar 

  8. Long, Y.: Index Theory for Symplectic Path with Applications. Progress in Mathematics, vol. 207. Birkhäuser, Basel (2002)

    Google Scholar 

  9. Schechter, M.: Rotationally invariant periodic solutions of semilinear wave equations. Abstr. Appl. Anal. 3, 171–180 (1998)

    Article  MathSciNet  Google Scholar 

  10. Wang, Q., Liu, C.: A new index theory for linear self-adjoint operator equations and its applications. J. Differ. Equ. 260, 3749–3784 (2016)

    Article  MathSciNet  Google Scholar 

  11. Watson, G.: A Treatise on the Theory of Bessel Functions, 2nd edn. Cambridge University Press, Cambridge (1952)

    Google Scholar 

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Liu, C. (2019). The Existence and Multiplicity of Solutions of Wave Equations. In: Index theory in nonlinear analysis. Springer, Singapore. https://doi.org/10.1007/978-981-13-7287-2_11

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