Dissipativity in the sense of Levinson for a class of second-order nonlinear evolution equations. (English) Zbl 0505.35012


35B35 Stability in context of PDEs
35B10 Periodic solutions to PDEs
35L70 Second-order nonlinear hyperbolic equations
35B45 A priori estimates in context of PDEs
34G20 Nonlinear differential equations in abstract spaces
Full Text: DOI


[1] Amerio, L.; Prouse, G., Abstract Almost Periodic Functions and Functional Equations (1971), Van Nostrand-Reinhold · Zbl 0215.15701
[2] Benilan, Ph; Brézis, H., Solutions faibles d’équations d’évolution dans les espaces de Hilbert, Annls. Inst. Fourier Univ. Grenoble, 22, 311-329 (1972) · Zbl 0226.47034
[3] Biroli, M., Bounded or almost periodic solutions of the nonlinear vibrating membrane equation, Ricerche Mat., 22, 190-202 (1973) · Zbl 0274.35042
[4] Biroli, M.; Haraux, A., Asymptotic behavior for an almost periodic, strongly dissipative wave equation, J. diff. Eqns., 38, 422-440 (1980) · Zbl 0413.35011
[5] Brézis, H., Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert (1973), North-Holland: North-Holland Amsterdam/London · Zbl 0252.47055
[6] Brézis, H., Problèmes unilatéraux, J. Math. pures appl., 51, 1-168 (1972) · Zbl 0237.35001
[7] Brézis, H.; Lions, J. L., Sur certains problèmes unilatéraux hyperboliques, C.r. Acad. Sci. Paris, Ser. A, 264, 928-931 (1967) · Zbl 0176.45901
[8] Brézis, H.; Nirenberg, L., Forced vibrations for a nonlinear wave equation, Communs pure appl. Math., 31, 1-30 (1978) · Zbl 0378.35040
[9] Ficken, F. A.; Fleishman, B. A., Initial value problems and time-periodic solutions for a nonlinear wave equation, Communs. pure appl. Math., 10, 331-356 (1957) · Zbl 0078.27602
[10] Haraux, A., Nonlinear evolution equations: global behavior of solutions, (Lecture Notes in Mathematics, 841 (1981), Springer: Springer Berlin) · Zbl 0583.35007
[12] Leray, J.; Schauder, J., Topologie et équations fonctionnelles, Annls scient. Ecole norm. sup. Paris, 51, 45-78 (1934) · JFM 60.0322.02
[13] Lions, J. L.; Strauss, W. A., Some nonlinear evolution equations, Bull Soc. math. France, 93, 43-96 (1965) · Zbl 0132.10501
[14] Prodi, G., Soluzioni periodiche della equazione delle onde con termine dissipativo non lineare, Rc. Semin. mat. Univ. Padova, 33 (1966) · Zbl 0145.35601
[15] Prouse, G., Soluzioni quasi periodiche della equazione delle onde con termine dissipativo non lineare, I, II, III, IV, Atti Accad. naz. Lincei Rc., 38-39 (1965)
[16] Strauss, W. A., On continuity of functions with values in various Banach spaces, Pacific J. Math., 19, 543-551 (1966) · Zbl 0185.20103
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.