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Curves of equiharmonic solutions, and problems at resonance
1. | Department Of Mathematical Sciences, University Of Cincinnati, Cincinnati Ohio 45221-0025 |
References:
[1] |
H. Amann and P. Hess, A multiplicity result for a class of elliptic boundary value problems, Proc. Roy. Soc. Edinburgh Sect. A, 84 (1979), 145-151.
doi: 10.1017/S0308210500017017. |
[2] |
A. Ambrosetti and G. Prodi, On the inversion of some differentiable mappings with singularities between Banach spaces, Ann. Mat. Pura Appl. (4), 93 (1972), 231-246.
doi: 10.1007/BF02412022. |
[3] |
J. A. Ambrosetti and G. Prodi, A Primer of Nonlinear Analysis, Cambridge Studies in Advanced Mathematics, 34, Cambridge University Press, Cambridge, 1993. |
[4] |
M. S. Berger and E. Podolak, On the solutions of a nonlinear Dirichlet problem, Indiana Univ. Math. J., 24 (1974/75), 837-846. |
[5] |
M. G. Crandall and P. H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rational Mech. Anal., 52 (1973), 161-180. |
[6] |
L. Evans, Partial Differential Equations, Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 1998. |
[7] |
D. G. de Figueiredo and W. M. Ni, Perturbations of second order linear elliptic problems by nonlinearities without Landesman-Lazer condition, Nonlinear Anal., 3 (1979), 629-634.
doi: 10.1016/0362-546X(79)90091-9. |
[8] |
R. Iannacci, M. N. Nkashama and J. R. Ward, Jr., Nonlinear second order elliptic partial differential equations at resonance, Trans. Amer. Math. Soc., 311 (1989), 711-726.
doi: 10.1090/S0002-9947-1989-0951886-3. |
[9] |
P. Korman, A global solution curve for a class of periodic problems, including the pendulum equation, Z. Angew. Math. Phys., 58 (2007), 749-766.
doi: 10.1007/s00033-006-6014-6. |
[10] |
P. Korman, Curves of equiharmonic solutions, and ranges of nonlinear equations, Adv. Differential Equations, 14 (2009), 963-984. |
[11] |
P. Korman, Global solution curves for boundary value problems, with linear part at resonance, Nonlinear Anal., 71 (2009), 2456-2467.
doi: 10.1016/j.na.2009.01.128. |
[12] |
E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech., 19 (1969/1970), 609-623. |
[13] |
A. C. Lazer and P. J. McKenna, On the number of solutions of a nonlinear Dirichlet problem, J. Math. Anal. Appl., 84 (1981), 282-294.
doi: 10.1016/0022-247X(81)90166-9. |
[14] |
L. Nirenberg, Topics in Nonlinear Functional Analysis, Lecture Notes, 1973-1974, Courant Institute of Mathematical Sciences, New York University, New York, 1974. |
show all references
References:
[1] |
H. Amann and P. Hess, A multiplicity result for a class of elliptic boundary value problems, Proc. Roy. Soc. Edinburgh Sect. A, 84 (1979), 145-151.
doi: 10.1017/S0308210500017017. |
[2] |
A. Ambrosetti and G. Prodi, On the inversion of some differentiable mappings with singularities between Banach spaces, Ann. Mat. Pura Appl. (4), 93 (1972), 231-246.
doi: 10.1007/BF02412022. |
[3] |
J. A. Ambrosetti and G. Prodi, A Primer of Nonlinear Analysis, Cambridge Studies in Advanced Mathematics, 34, Cambridge University Press, Cambridge, 1993. |
[4] |
M. S. Berger and E. Podolak, On the solutions of a nonlinear Dirichlet problem, Indiana Univ. Math. J., 24 (1974/75), 837-846. |
[5] |
M. G. Crandall and P. H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rational Mech. Anal., 52 (1973), 161-180. |
[6] |
L. Evans, Partial Differential Equations, Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 1998. |
[7] |
D. G. de Figueiredo and W. M. Ni, Perturbations of second order linear elliptic problems by nonlinearities without Landesman-Lazer condition, Nonlinear Anal., 3 (1979), 629-634.
doi: 10.1016/0362-546X(79)90091-9. |
[8] |
R. Iannacci, M. N. Nkashama and J. R. Ward, Jr., Nonlinear second order elliptic partial differential equations at resonance, Trans. Amer. Math. Soc., 311 (1989), 711-726.
doi: 10.1090/S0002-9947-1989-0951886-3. |
[9] |
P. Korman, A global solution curve for a class of periodic problems, including the pendulum equation, Z. Angew. Math. Phys., 58 (2007), 749-766.
doi: 10.1007/s00033-006-6014-6. |
[10] |
P. Korman, Curves of equiharmonic solutions, and ranges of nonlinear equations, Adv. Differential Equations, 14 (2009), 963-984. |
[11] |
P. Korman, Global solution curves for boundary value problems, with linear part at resonance, Nonlinear Anal., 71 (2009), 2456-2467.
doi: 10.1016/j.na.2009.01.128. |
[12] |
E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech., 19 (1969/1970), 609-623. |
[13] |
A. C. Lazer and P. J. McKenna, On the number of solutions of a nonlinear Dirichlet problem, J. Math. Anal. Appl., 84 (1981), 282-294.
doi: 10.1016/0022-247X(81)90166-9. |
[14] |
L. Nirenberg, Topics in Nonlinear Functional Analysis, Lecture Notes, 1973-1974, Courant Institute of Mathematical Sciences, New York University, New York, 1974. |
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