Periodic solutions of the third order parametric differential equations involving large nonlinearities

Ján Andres; Vladimír Vlček

Mathematica Slovaca (1991)

  • Volume: 41, Issue: 4, page 337-349
  • ISSN: 0232-0525

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Andres, Ján, and Vlček, Vladimír. "Periodic solutions of the third order parametric differential equations involving large nonlinearities." Mathematica Slovaca 41.4 (1991): 337-349. <http://eudml.org/doc/34324>.

@article{Andres1991,
author = {Andres, Ján, Vlček, Vladimír},
journal = {Mathematica Slovaca},
keywords = {periodic solutions; parametric third order equations; instability criteria},
language = {eng},
number = {4},
pages = {337-349},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Periodic solutions of the third order parametric differential equations involving large nonlinearities},
url = {http://eudml.org/doc/34324},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Andres, Ján
AU - Vlček, Vladimír
TI - Periodic solutions of the third order parametric differential equations involving large nonlinearities
JO - Mathematica Slovaca
PY - 1991
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 41
IS - 4
SP - 337
EP - 349
LA - eng
KW - periodic solutions; parametric third order equations; instability criteria
UR - http://eudml.org/doc/34324
ER -

References

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  2. VILLARI G., Contributi alio studio dell' esistenza di soluzioni periodiche per i sistemi di equazioni differenziali ordinarie, Ann. Mat. Pura Appl. 69 (1965), 171-190. (1965) MR0190452
  3. REISSIG R., SANSONE G., CONTI R., Nichtlineare Differentialgleichungen höherer Ordnung, Cremonese, Roma, 1969. (1969) Zbl0172.10801MR0241749
  4. EZEILO J. O. C, A further result on the existence of periodic solutions on the equation x"' + ax" + bx' + h(x) = p(t, x, x', x"), Math. Proc. Camb. Philos. Soc. 77 (1975), 547-551. (1975) MR0361285
  5. EZEILO J. O. C., Further results on the existence of periodic solutions of a certain third order differential equation, Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 64 (1978), 48-58. (1978) Zbl0405.34042MR0542152
  6. EZEILO J. O. C., Periodic solutions of third-order differential equations in the past twenty five years or so, In: Invited paper presented at the 2nd Pan-African Congress of the African Mathematical Union, 23-29 March 1986, University of Jos, Nigeria. (1986) 
  7. KONSTANTINOV M. S., Existence of periodic solutions of certain differential equation, (Russian), Differ. Uravn., Sb. Tr. Mat. Kafedr Pedinst. RSFSR 9 (1977), 48-56. (1977) MR0486815
  8. KONSTANTINOV M. S., On a third order equation, (Russian), Differ. Uravn., Sb. Tr. Mat. Kafedr Pedinst. RSFSR 11 (1978), 93-99. (1978) MR0512943
  9. KONSTANTINOV M. S., Some sufficient conditions for existence of periodic and bounded solutions of the equation x'" + ax' + g(x') + cx = Ψ(t, x, x',x"), (Russian), In: Diff. Urav. Qualitative Theory, ed I. P. Makarov. Rjazan. Gos. Ped. Inst., Rjazan, 1984, pp. 92-100. (1984) MR0843088
  10. ANDRES J., VORÁČEK J., Periodic solutions to a nonlinear parametric differential equation of the third order, Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 77 (1984), 81-86. (1984) Zbl0607.34039MR0884940
  11. MEHRI B., On the existence of periodic solutions for certain nonlinear differential equation, Rev. Roum. Math. Pures Appl. 23 (1978), 1367-1373. (1978) MR0522593
  12. ANDRES J., Periodic boundary value problems for certain nonlinear differential equations of the third order, Math. Slovaca 35 (1985), 305-309. (1985) MR0808366
  13. EZEILO J. O. C., ONYA J., Non-resonant oscillations for third-order differential equations, J. Nig. Math. Soc. 3 (1984), 83-96. (1984) 
  14. EZEILO J. O. C., NKASHAMA M. N., Non-uniform non-resonance and existence of periodic solutions of some third order non-linear ordinary differential equations, Nonlinear Anal., Theory Methods Appl. 12 (1988), 1029-1046. (1988) 
  15. EZEILO J. O. C., OMARI P., Non-resonant oscillations for some third-order differential equations II, In: ICTP, Trieste IC/87/374 (1987). (1987) 
  16. FONDA A., HABETS P., Periodic solutions of asymptotically positively homogeneous differential equations, Rapp., Semin. Math. Appl. Mec, Univ. Cathol. Louvain No. 130 (1988). (1988) MR1012200
  17. AFUWAPE A. U., OMARI P., ZANOLIN F., Nonlinear perturbations of differential operators with nontrivial kernel and applications to third order periodic boundary value problems, J. Math. Anal. Appl. 143 (1989), 35-56. (1989) MR1019448
  18. AFTABIZADEH A. R., XU J.-M., GUPTA C. P., Periodic boundary value problems for third order ordinary differential equations, Nonlinear Anal., Theory Methods Appl. 14 (1990), 1-10. (1990) Zbl0706.34018MR1028242
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