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Threshold asymptotic behaviors for a delayed nonlocal reaction-diffusion model of mistletoes and birds in a 2D strip
Classification of bifurcation curves of positive solutions for a nonpositone problem with a quartic polynomial
1. | Department of Applied Mathematics, National University of Tainan, Tainan 700, Taiwan, Taiwan |
References:
[1] |
I. Addou and S.-H. Wang, Exact multiplicity results for a $p$-Laplacian problem with concave-convex-concave nonlinearities, Nonlinear Anal., 53 (2003), 111-137.
doi: 10.1016/S0362-546X(02)00298-5. |
[2] |
M.G. Crandall and P.H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rational Mech. Anal., 52 (1973), 161-180. |
[3] |
K.-C. Hung and S.-H. Wang, Global bifurcation and exact multiplicity of positive solutions for a positone problem with cubic nonlinearity and their applications, Trans. Amer. Math. Soc., 365 (2013), 1933-1956.
doi: 10.1090/S0002-9947-2012-05670-4. |
[4] |
P. Korman, Y. Li and T. Ouyang, Exact multiplicity results for boundary value problems with nonlinearities generalising cubic, Proc. Roy. Soc. Edinburgh Sect. A, 126 (1996), 599-616.
doi: 10.1017/S0308210500022927. |
[5] |
T. Laetsch, The number of solutions of a nonlinear two point boundary value problem, Indiana Univ. Math. J., 20 (1970), 1-13. |
[6] |
J. Shi, Multi-parameter bifurcation and applications, in ICM2002 Satellite Conference on Nonlinear Functional Analysis: Topological Methods, Variational Methods and Their Applications (H. Brezis, K.C. Chang, S.J. Li and P. Rabinowitz Eds.), World Scientific, Singapore, (2003), 211-222. |
[7] |
J. Smoller and A. Wasserman, Global bifurcation of steady-state solutions, J. Differential Equations, 39 (1981), 269-290.
doi: 10.1016/0022-0396(81)90077-2. |
[8] |
C.-C. Tzeng, K.-C. Hung and S.-H. Wang, Global bifurcation and exact multiplicity of positive solutions for a positone problem with cubic nonlinearity, J. Differential Equations, 252 (2012), 6250-6274.
doi: 10.1016/j.jde.2012.02.020. |
[9] |
S.-H. Wang, A correction for a paper by J. Smoller and A. Wasserman, J. Differential Equations, 77 (1989), 199-202.
doi: 10.1016/0022-0396(89)90162-9. |
[10] |
S.-H. Wang and N. D. Kazarinoff, Bifurcation and stability of positive solutions of a two-point boundary value problem, J. Austral. Math. Soc. Ser. A, 52 (1992), 334-342. |
[11] |
S.-H. Wang and N. D. Kazarinoff, Bifurcation of steady-state solutions of a scalar reaction-diffusion equation in one space variable, J. Austral. Math. Soc. Ser. A, 52 (1992), 343-355. |
[12] |
S.-H. Wang and T.-S. Yeh, S-shaped and broken S-shaped bifurcation diagrams with hysteresis for a multiparameter spruce budworm population problem in one space dimension, J. Differential Equations, 255 (2013), 812-839.
doi: 10.1016/j.jde.2013.05.004. |
show all references
References:
[1] |
I. Addou and S.-H. Wang, Exact multiplicity results for a $p$-Laplacian problem with concave-convex-concave nonlinearities, Nonlinear Anal., 53 (2003), 111-137.
doi: 10.1016/S0362-546X(02)00298-5. |
[2] |
M.G. Crandall and P.H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rational Mech. Anal., 52 (1973), 161-180. |
[3] |
K.-C. Hung and S.-H. Wang, Global bifurcation and exact multiplicity of positive solutions for a positone problem with cubic nonlinearity and their applications, Trans. Amer. Math. Soc., 365 (2013), 1933-1956.
doi: 10.1090/S0002-9947-2012-05670-4. |
[4] |
P. Korman, Y. Li and T. Ouyang, Exact multiplicity results for boundary value problems with nonlinearities generalising cubic, Proc. Roy. Soc. Edinburgh Sect. A, 126 (1996), 599-616.
doi: 10.1017/S0308210500022927. |
[5] |
T. Laetsch, The number of solutions of a nonlinear two point boundary value problem, Indiana Univ. Math. J., 20 (1970), 1-13. |
[6] |
J. Shi, Multi-parameter bifurcation and applications, in ICM2002 Satellite Conference on Nonlinear Functional Analysis: Topological Methods, Variational Methods and Their Applications (H. Brezis, K.C. Chang, S.J. Li and P. Rabinowitz Eds.), World Scientific, Singapore, (2003), 211-222. |
[7] |
J. Smoller and A. Wasserman, Global bifurcation of steady-state solutions, J. Differential Equations, 39 (1981), 269-290.
doi: 10.1016/0022-0396(81)90077-2. |
[8] |
C.-C. Tzeng, K.-C. Hung and S.-H. Wang, Global bifurcation and exact multiplicity of positive solutions for a positone problem with cubic nonlinearity, J. Differential Equations, 252 (2012), 6250-6274.
doi: 10.1016/j.jde.2012.02.020. |
[9] |
S.-H. Wang, A correction for a paper by J. Smoller and A. Wasserman, J. Differential Equations, 77 (1989), 199-202.
doi: 10.1016/0022-0396(89)90162-9. |
[10] |
S.-H. Wang and N. D. Kazarinoff, Bifurcation and stability of positive solutions of a two-point boundary value problem, J. Austral. Math. Soc. Ser. A, 52 (1992), 334-342. |
[11] |
S.-H. Wang and N. D. Kazarinoff, Bifurcation of steady-state solutions of a scalar reaction-diffusion equation in one space variable, J. Austral. Math. Soc. Ser. A, 52 (1992), 343-355. |
[12] |
S.-H. Wang and T.-S. Yeh, S-shaped and broken S-shaped bifurcation diagrams with hysteresis for a multiparameter spruce budworm population problem in one space dimension, J. Differential Equations, 255 (2013), 812-839.
doi: 10.1016/j.jde.2013.05.004. |
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