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On the Bonheure-Noris-Weth conjecture in the case of linearly bounded nonlinearities
1. | Department of Mathematics, Northwest Normal University, Lanzhou, 730070 |
2. | Department of Mathematics, Northwest Normal University, Lanzhou 730070, China |
References:
[1] |
D. Bonheure, B. Noris and T. Weth, Increasing radial solutions for Neumann problems without growth restrictions, Ann. Inst. H. Poincaré Anal. Non Linéaire, 29 (2012), 573-588.
doi: 10.1016/j.anihpc.2012.02.002. |
[2] |
D. Bonheure, E. Serra and P. Tilli, Radial positive solutions of elliptic systems with Neumann boundary conditions, J. Funct. Anal., 265 (2013), 375-398.
doi: 10.1016/j.jfa.2013.05.027. |
[3] |
G. Dai and R. Ma, Unilateral global bifurcation phenomena and nodal solutions for $p$-Laplacian, J. Differential Equations, 252 (2012), 2448-2468.
doi: 10.1016/j.jde.2011.09.026. |
[4] |
E. N. Dancer, Bifurcation from simple eigenvalues and eigenvalues of geometric multiplicity one, Bull. Lond. Math. Soc., 34 (2002), 533-538.
doi: 10.1112/S002460930200108X. |
[5] |
E. N. Dancer, On the structure of solutions of non-linear eigenvalue problems, Indiana Univ. Math. J., 23 (1973/74), 1069-1076. |
[6] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 edition, Springer-Verlag, Berlin, 2001. |
[7] |
A. C. Lazer and P. J. Mckenna, Global bifurcation and a theorem of Tarantello, J. Math. Anal. Appl., 181 (1994), 648-655. MR1264537
doi: 10.1006/jmaa.1994.1049. |
[8] |
J. López-Gómez, Spectral Theory and Nonlinear Functional Analysis, in: Research Notes in Mathematics, vol. 426, Chapman & Hall/CRC, Boca Raton, Florida, 2001. |
[9] |
R. Ma and B. Thompson, Nodal solutions for nonlinear eigenvalue problems, Nonlinear Anal., 59 (2004), 707-718.
doi: 10.1016/S0362-546X(04)00280-9. |
[10] |
A. Miciano and R. Shivaji, Multiple positive solutions for a class of semipositone Neumann two point boundary value problems, J. Math. Anal. Appl., 178 (1993), 102-115.
doi: 10.1006/jmaa.1993.1294. |
[11] |
L. A. Peletier and J. Serrin, Uniqueness of positive solutions of semilinear equations in $\mathbb{R}^{N}$, Arch. Rational Mech. Anal., 81 (1983), 181-197.
doi: 10.1007/BF00250651. |
[12] |
M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Springer-Verlag, New York, 1984. |
[13] |
P. H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal., 7 (1971), 487-513.
doi: 10.1016/0022-1236(71)90030-9. |
[14] |
E. Serra and P. Tilli, Monotonicity constraints and supercritical Neumann problems, Ann. Inst. H. Poincaré Anal. Non Linéaire, 28 (2011), 63-74.
doi: 10.1016/j.anihpc.2010.10.003. |
[15] |
W. Walter, Ordinary Differential Equations, Translated from the sixth German (1996) edition by Russell Thompson. Graduate Texts in Mathematics 182. Springer-Verlag, New York, 1998. |
show all references
References:
[1] |
D. Bonheure, B. Noris and T. Weth, Increasing radial solutions for Neumann problems without growth restrictions, Ann. Inst. H. Poincaré Anal. Non Linéaire, 29 (2012), 573-588.
doi: 10.1016/j.anihpc.2012.02.002. |
[2] |
D. Bonheure, E. Serra and P. Tilli, Radial positive solutions of elliptic systems with Neumann boundary conditions, J. Funct. Anal., 265 (2013), 375-398.
doi: 10.1016/j.jfa.2013.05.027. |
[3] |
G. Dai and R. Ma, Unilateral global bifurcation phenomena and nodal solutions for $p$-Laplacian, J. Differential Equations, 252 (2012), 2448-2468.
doi: 10.1016/j.jde.2011.09.026. |
[4] |
E. N. Dancer, Bifurcation from simple eigenvalues and eigenvalues of geometric multiplicity one, Bull. Lond. Math. Soc., 34 (2002), 533-538.
doi: 10.1112/S002460930200108X. |
[5] |
E. N. Dancer, On the structure of solutions of non-linear eigenvalue problems, Indiana Univ. Math. J., 23 (1973/74), 1069-1076. |
[6] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 edition, Springer-Verlag, Berlin, 2001. |
[7] |
A. C. Lazer and P. J. Mckenna, Global bifurcation and a theorem of Tarantello, J. Math. Anal. Appl., 181 (1994), 648-655. MR1264537
doi: 10.1006/jmaa.1994.1049. |
[8] |
J. López-Gómez, Spectral Theory and Nonlinear Functional Analysis, in: Research Notes in Mathematics, vol. 426, Chapman & Hall/CRC, Boca Raton, Florida, 2001. |
[9] |
R. Ma and B. Thompson, Nodal solutions for nonlinear eigenvalue problems, Nonlinear Anal., 59 (2004), 707-718.
doi: 10.1016/S0362-546X(04)00280-9. |
[10] |
A. Miciano and R. Shivaji, Multiple positive solutions for a class of semipositone Neumann two point boundary value problems, J. Math. Anal. Appl., 178 (1993), 102-115.
doi: 10.1006/jmaa.1993.1294. |
[11] |
L. A. Peletier and J. Serrin, Uniqueness of positive solutions of semilinear equations in $\mathbb{R}^{N}$, Arch. Rational Mech. Anal., 81 (1983), 181-197.
doi: 10.1007/BF00250651. |
[12] |
M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Springer-Verlag, New York, 1984. |
[13] |
P. H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal., 7 (1971), 487-513.
doi: 10.1016/0022-1236(71)90030-9. |
[14] |
E. Serra and P. Tilli, Monotonicity constraints and supercritical Neumann problems, Ann. Inst. H. Poincaré Anal. Non Linéaire, 28 (2011), 63-74.
doi: 10.1016/j.anihpc.2010.10.003. |
[15] |
W. Walter, Ordinary Differential Equations, Translated from the sixth German (1996) edition by Russell Thompson. Graduate Texts in Mathematics 182. Springer-Verlag, New York, 1998. |
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