논문KCI 등재
Multiple periodic solutions of second-order ordinary differential equations across resonance
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In this paper we study the existence of multiple periodic solutions of second-order ordinary differential equations. New results of multiplicity of periodic solutions are obtained when the nonlinearity may cross multiple consecutive eigenvalues. The arguments are proceeded by a combination of variational and degree theoretic methods.
Abstract
In this paper we study the existence of multiple periodic solutions of second-order ordinary differential equations. New results of multiplicity of periodic solutions are obtained when the nonlinearity may cross multiple consecutive eigenvalues. The arguments are proceeded by a combination of variational and degree theoretic methods.
참고문헌 (30)
- H. Amann, "A note on degree theory for gradient mappings", Proc. Amer. Math. Soc, 85(4), pp.591~595 (1982)
- G. Barletta, "Periodic problems with double resonance", NoDEA Nonlinear Differential Equations Appl, 19(3), pp.303~328 (2012)
- A. Castro, "Multiple solutions for a nonlinear Dirichlet problem", SIAM J. Math. Anal, 25(6), pp.1554~1561 (1994)
- X. J. Chang, "Two-point boundary value problems for Duffing equations across resonance", J. Optim. Theory Appl, 140(3), pp.419~430 (2009)
- X. J. Chang, "Existence and multiplicity of nontrivial solutions for semilinear elliptic Dirichlet problems across resonance, Topol", Methods Nonlinear Anal, 36(2), pp.285~310 (2010)
- X. J. Chang, "Nonresonance conditions on the potential with respect to the Fuˇc´ık spectrum for semilinear Dirichlet problems", Z. Angew. Math. Phys, 61(5), pp.823~833 (2010)
- X. J. Chang, "Existence of periodic solutions for a class of p-Laplacian equations", Bound. Value Probl, 2013, pp.11~ (2013)
- D. G. Costa, "Existence of solution for a class of semilinear elliptic problems at double resonance", Bol. Soc. Brasil. Mat, 19(1), pp.21~37 (1988)
- D. Del Santo, "Nonresonance conditions on the potential for a semilinear elliptic problem", J. Differential Equations, 108(1), pp.120~138 (1994)
- T. Ding, "Existence and multiplicity results for periodic solutions of semilinear Duffing equations", J. Differential Equations, 105(2), pp.364~409 (1993)
- C. L. Dolph, "Nonlinear integral equations of the Hammerstein type", Trans. Amer. Math. Soc, 66, pp.289~307 (1949)
- P. Dr´abek, "Landesman-Lazer conditions for nonlinear problems with jumping nonlin-earities", J. Differential Equations, 85(1), pp.186~199 (1990)
- P. Habets, "Existence of periodic solutions of Duffing equations", J. Dif-ferential Equations, 78(1), pp.1~32 (1989)
- P. Habets, "Nonresonance conditions on the potential with respect to the Fuik spectrum for the periodic boundary value problem", Rocky Mountain J. Math, 25(4), pp.1305~1340 (1995)
- C. Fabry, "Periodic solutions of nonlinear differential equations with double resonance", Ann. Mat. Pura Appl, (4) 157, pp.99~116 (1990)
- A. Fonda, "On the existence of periodic solutions for scalar second order differential equations when only the asymptotic behaviour of the potential is known", Proc. Amer. Math. Soc, 119(2), pp.439~445 (1993)
- A. Fonda, "Periodic solutions of asymptotically positively homogeneous differential equations", J. Differential Equations, 81(1), pp.68~97 (1989)
- D. Y. Hao, "Semilinear Duffing equations crossing resonance points", J. Differential Equations, 133(1), pp.98~116 (1997)
- H. Hofer, "The topological degree at a critical point of mountain pass type, Nonlinear functional analysis and its applications, Part 1 (Berkeley, Calif., 1983)", Proc. Sympos. Pure Math, 45, pp.501~509 (1986), Amer. Math. Soc
- R. Iannacci, "Unbounded perturbations of forced second order or-dinary differential equations at resonance", J. Differential Equations, 69(3), pp.289~301 (1987)
- E. M. Landesman, "Nonlinear perturbations of linear elliptic boundary value problems at resonance", J. Math. Mech, 19, pp.609~623 (1969)
- A. C. Lazer, "Nontrivial solutions of operator equations and morse indices of critical points of min-max type", Nonlinear Anal, 12(8), pp.761~775 (1988)
- W. B. Liu, "Existence of 2-periodic solutions for the non-dissipative Duffing equation under asymptotic behaviors of potential function", Z. Angew. Math. Phys, 57(1), pp.1~11 (2006)
- J. Mawhin, "Critical Point Theory and Hamiltonian Systems" (1989), Spring-Verlag
- L. Nirenberg, "Topics in Nonlinear Functional Analysis, Courant Institute of Mathemat-ical Sciences" (1974), New York University
- P. Omari, "Nonresonance conditions on the potential for a second-order periodic boundary value problem", Proc. Amer. Math. Soc, 117(1), pp.125~135 (1993)
- N. S. Papageorgiou, "Multiple nontrivial solutions for doubly resonant periodic problems", Canad. Math. Bull, 53(2), pp.347~359 (2010)
- J. Su, "Multiple periodic solutions of ordinary differential equations with double resonance", Nonlinear Anal, 70(4), pp.1520~1527 (2009)
- M. R. Zhang, "Nonresonance conditions for asymptotically positively homogeneous dif-ferential systems: the Fuˇc´ık spectrum and its generalization", J. Differential Equations, 145(2), pp.332~366 (1998)
- X. Zhao, "Existence of anti-periodic solutions for second-order ordinary differential equations involving the Fuˇc´ık spectrum", Bound. Value Probl, 2012, pp.12~ (2012)
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