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Classification of bifurcation diagrams of a $P$-Laplacian nonpositone problem
1. | Department of Mathematics, National Tsing Hua University, Hsinchu 300, Taiwan |
2. | Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300 |
3. | Department of Applied Mathematics, National University of Tainan, Tainan 700, Taiwan |
References:
[1] |
J. G. Cheng, Exact number of positive solutions for a class of semipositone problems, J. Math. Anal. Appl., 280 (2003), 197-208.
doi: 10.1016/S0022-247X(02)00539-5. |
[2] |
J. G. Cheng, Uniqueness results for the one-dimensional $p$-Laplacian, J. Math. Anal. Appl., 311 (2005), 381-388.
doi: 10.1016/j.jmaa.2005.02.057. |
[3] |
J. G. Cheng, Exact number of positive solutions for semipositone problems, J. Math. Anal. Appl., 313 (2006), 322-341.
doi: 10.1016/j.jmaa.2005.09.043. |
[4] |
J. I. Díaz, "Nonlinear Partial Differential Equations and Free Boundaries, Vol. I. Elliptic Equations," Research Notes in Mathematics, 106, Pitman, Boston, MA, 1985. |
[5] |
J. I. Díaz, Qualitative study of nonlinear parabolic equations: an introduction, Extracta Math., 16 (2001), 303-341. |
[6] |
J. I. Díaz and J. Hernández, Global bifurcation and continua of nonnegative solutions for a quasilinear elliptic problem, C. R. Acad. Sci. Paris Sér. I Math., 329 (1999), 587-592.
doi: 10.1016/S0764-4442(00)80006-3. |
[7] |
J. I. Díaz, J. Hernández and F. J. Mancebo, Branches of positive and free boundary solutions for some singular quasilinear elliptic problems, J. Math. Anal. Appl., 352 (2009), 449-474.
doi: 10.1016/j.jmaa.2008.07.073. |
[8] |
T. Laetsch, The number of solutions of a nonlinear two point boundary value problem, Indiana Univ. Math. J., 20 (1970), 1-13. |
[9] |
A. Lakmeche and A. Hammoudi, Multiple positive solutions of the one-dimensional $p$-Laplacian, J. Math. Anal. Appl., 317 (2006), 43-49.
doi: 10.1016/j.jmaa.2005.10.040. |
[10] | |
[11] |
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. |
[12] |
S.-H. Wang and T.-S. Yeh, A complete classification of bifurcation diagrams of a Dirichlet problem with concave-convex nonlinearities, J. Math. Anal. Appl., 291 (2004), 128-153.
doi: 10.1016/j.jmaa.2003.10.021. |
[13] |
Z. L. Wei and C. C. Pang, Exact structure of positive solutions for some $p$-Laplacian equations, J. Math. Anal. Appl., 301 (2005), 52-64.
doi: 10.1016/j.jmaa.2004.06.058. |
[14] |
R. L. Wheeden and A. Zygmund, "Measure and Integral: An Introduction to Real Analysis," Marcel Dekker, New York, 1977. |
show all references
References:
[1] |
J. G. Cheng, Exact number of positive solutions for a class of semipositone problems, J. Math. Anal. Appl., 280 (2003), 197-208.
doi: 10.1016/S0022-247X(02)00539-5. |
[2] |
J. G. Cheng, Uniqueness results for the one-dimensional $p$-Laplacian, J. Math. Anal. Appl., 311 (2005), 381-388.
doi: 10.1016/j.jmaa.2005.02.057. |
[3] |
J. G. Cheng, Exact number of positive solutions for semipositone problems, J. Math. Anal. Appl., 313 (2006), 322-341.
doi: 10.1016/j.jmaa.2005.09.043. |
[4] |
J. I. Díaz, "Nonlinear Partial Differential Equations and Free Boundaries, Vol. I. Elliptic Equations," Research Notes in Mathematics, 106, Pitman, Boston, MA, 1985. |
[5] |
J. I. Díaz, Qualitative study of nonlinear parabolic equations: an introduction, Extracta Math., 16 (2001), 303-341. |
[6] |
J. I. Díaz and J. Hernández, Global bifurcation and continua of nonnegative solutions for a quasilinear elliptic problem, C. R. Acad. Sci. Paris Sér. I Math., 329 (1999), 587-592.
doi: 10.1016/S0764-4442(00)80006-3. |
[7] |
J. I. Díaz, J. Hernández and F. J. Mancebo, Branches of positive and free boundary solutions for some singular quasilinear elliptic problems, J. Math. Anal. Appl., 352 (2009), 449-474.
doi: 10.1016/j.jmaa.2008.07.073. |
[8] |
T. Laetsch, The number of solutions of a nonlinear two point boundary value problem, Indiana Univ. Math. J., 20 (1970), 1-13. |
[9] |
A. Lakmeche and A. Hammoudi, Multiple positive solutions of the one-dimensional $p$-Laplacian, J. Math. Anal. Appl., 317 (2006), 43-49.
doi: 10.1016/j.jmaa.2005.10.040. |
[10] | |
[11] |
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. |
[12] |
S.-H. Wang and T.-S. Yeh, A complete classification of bifurcation diagrams of a Dirichlet problem with concave-convex nonlinearities, J. Math. Anal. Appl., 291 (2004), 128-153.
doi: 10.1016/j.jmaa.2003.10.021. |
[13] |
Z. L. Wei and C. C. Pang, Exact structure of positive solutions for some $p$-Laplacian equations, J. Math. Anal. Appl., 301 (2005), 52-64.
doi: 10.1016/j.jmaa.2004.06.058. |
[14] |
R. L. Wheeden and A. Zygmund, "Measure and Integral: An Introduction to Real Analysis," Marcel Dekker, New York, 1977. |
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