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semigroup; evolution equation; invariant set; Conley index; resonance

References:

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[2] Ćwiszewski, A., Rybakowski, K. P.: **Singular dynamics of strongly damped beam equation**. J. Differ. Equations 247 (2009), 3202-3233. DOI 10.1016/j.jde.2009.09.006 | MR 2571574 | Zbl 1187.35002

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[4] Kokocki, P.: **The averaging principle and periodic solutions for nonlinear evolution equations at resonance**. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 85 (2013), 253-278. DOI 10.1016/j.na.2013.02.030 | MR 3040364 | Zbl 1292.34059

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[8] Landesman, E. M., Lazer, A. C.: **Nonlinear perturbations of linear elliptic boundary value problems at resonance**. J. Math. Mech. 19 (1969/1970), 609-623. MR 0267269

[9] Massatt, P.: **Limiting behavior for strongly damped nonlinear wave equations. Nonlinear phenomena in mathematical sciences, Proc. Int. Conf., Arlington/Tex., 1980**. J. Differential Equations 48 (1982), 334-349. DOI 10.1016/0022-0396(83)90098-0 | MR 0702424

[10] Prizzi, M.: **On admissibility for parabolic equations in {$\mathbb R^n$}**. Fundam. Math. 176 (2003), 261-275. DOI 10.4064/fm176-3-5 | MR 1992823

[11] Rybakowski, K. P.: **The Homotopy Index and Partial Differential Equations**. Universitext Springer, Berlin (1987). MR 0910097 | Zbl 0628.58006

[12] Rybakowski, K. P.: **Nontrivial solutions of elliptic boundary value problems with resonance at zero**. Ann. Mat. Pura Appl. (4) 139 (1985), 237-277. MR 0798176 | Zbl 0572.35037