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Strong coincidence and overlap coincidence
Positive solutions to indefinite Neumann problems when the weight has positive average
1. | Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, I-10123 Torino, Italy |
2. | Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Cozzi 55, I-20125 Milano, Italy |
References:
[1] |
S. Alama and G. Tarantello, On semilinear elliptic equations with indefinite nonlinearities, Calc. Var. Partial Differential Equations, 1 (1993), 439-475.
doi: 10.1007/BF01206962. |
[2] |
H. Amann, On the number of solutions of nonlinear equations in ordered Banach spaces, J. Functional Analysis, 11 (1972), 346-384.
doi: 10.1016/0022-1236(72)90074-2. |
[3] |
H. Amann and J. López-Gómez, A priori bounds and multiple solutions for superlinear indefinite elliptic problems, J. Differential Equations, 146 (1998), 336-374.
doi: 10.1006/jdeq.1998.3440. |
[4] |
F. V. Atkinson, W. N. Everitt and K. S. Ong, On the $m$-coefficient of Weyl for a differential equation with an indefinite weight function, Proc. London Math. Soc. (3), 29 (1974), 368-384. |
[5] |
C. Bandle, M. A. Pozio and A. Tesei, Existence and uniqueness of solutions of nonlinear Neumann problems, Math. Z., 199 (1988), 257-278.
doi: 10.1007/BF01159655. |
[6] |
H. Berestycki, I. Capuzzo-Dolcetta and L. Nirenberg, Superlinear indefinite elliptic problems and nonlinear Liouville theorems, Topol. Methods Nonlinear Anal., 4 (1994), 59-78. |
[7] |
H. Berestycki, I. Capuzzo-Dolcetta and L. Nirenberg, Variational methods for indefinite superlinear homogeneous elliptic problems, NoDEA Nonlinear Differential Equations Appl., 2 (1995), 553-572.
doi: 10.1007/BF01210623. |
[8] |
A. Boscaggin, G. Feltrin and F. Zanolin, Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: A topological degree approach for the super-sublinear case, Proc. Roy. Soc. Edinburgh Sect. A., 146 (2016), 449-474.
doi: 10.1017/S0308210515000621. |
[9] |
A. Boscaggin and M. Garrione, Multiple solutions to Neumann problems with indefinite weight and bounded nonlinearities, J. Dynam. Differential Equations, 28 (2016), 167-187.
doi: 10.1007/s10884-015-9430-5. |
[10] |
A. Boscaggin and F. Zanolin, Pairs of positive periodic solutions of second order nonlinear equations with indefinite weight, J. Differential Equations, 252 (2012), 2900-2921.
doi: 10.1016/j.jde.2011.09.011. |
[11] |
A. Boscaggin and F. Zanolin, Second order ordinary differential equations with indefinite weight: the Neumann boundary value problem, Ann. Mat. Pura Appl. (4), 194 (2015), 451-478.
doi: 10.1007/s10231-013-0384-0. |
[12] |
G. Feltrin and F. Zanolin, Existence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems, Adv. Differential Equations, 20 (2015), 937-982. |
[13] |
P. Hess and T. Kato, On some linear and nonlinear eigenvalue problems with an indefinite weight function, Comm. Partial Differential Equations, 5 (1980), 999-1030.
doi: 10.1080/03605308008820162. |
[14] |
J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Applied Mathematical Sciences, 74, Springer-Verlag, New York, 1989.
doi: 10.1007/978-1-4757-2061-7. |
[15] |
P. H. Rabinowitz, Pairs of positive solutions of nonlinear elliptic partial differential equations,, Indiana Univ. Math. J., 23 (): 173.
doi: 10.1512/iumj.1974.23.23014. |
show all references
References:
[1] |
S. Alama and G. Tarantello, On semilinear elliptic equations with indefinite nonlinearities, Calc. Var. Partial Differential Equations, 1 (1993), 439-475.
doi: 10.1007/BF01206962. |
[2] |
H. Amann, On the number of solutions of nonlinear equations in ordered Banach spaces, J. Functional Analysis, 11 (1972), 346-384.
doi: 10.1016/0022-1236(72)90074-2. |
[3] |
H. Amann and J. López-Gómez, A priori bounds and multiple solutions for superlinear indefinite elliptic problems, J. Differential Equations, 146 (1998), 336-374.
doi: 10.1006/jdeq.1998.3440. |
[4] |
F. V. Atkinson, W. N. Everitt and K. S. Ong, On the $m$-coefficient of Weyl for a differential equation with an indefinite weight function, Proc. London Math. Soc. (3), 29 (1974), 368-384. |
[5] |
C. Bandle, M. A. Pozio and A. Tesei, Existence and uniqueness of solutions of nonlinear Neumann problems, Math. Z., 199 (1988), 257-278.
doi: 10.1007/BF01159655. |
[6] |
H. Berestycki, I. Capuzzo-Dolcetta and L. Nirenberg, Superlinear indefinite elliptic problems and nonlinear Liouville theorems, Topol. Methods Nonlinear Anal., 4 (1994), 59-78. |
[7] |
H. Berestycki, I. Capuzzo-Dolcetta and L. Nirenberg, Variational methods for indefinite superlinear homogeneous elliptic problems, NoDEA Nonlinear Differential Equations Appl., 2 (1995), 553-572.
doi: 10.1007/BF01210623. |
[8] |
A. Boscaggin, G. Feltrin and F. Zanolin, Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: A topological degree approach for the super-sublinear case, Proc. Roy. Soc. Edinburgh Sect. A., 146 (2016), 449-474.
doi: 10.1017/S0308210515000621. |
[9] |
A. Boscaggin and M. Garrione, Multiple solutions to Neumann problems with indefinite weight and bounded nonlinearities, J. Dynam. Differential Equations, 28 (2016), 167-187.
doi: 10.1007/s10884-015-9430-5. |
[10] |
A. Boscaggin and F. Zanolin, Pairs of positive periodic solutions of second order nonlinear equations with indefinite weight, J. Differential Equations, 252 (2012), 2900-2921.
doi: 10.1016/j.jde.2011.09.011. |
[11] |
A. Boscaggin and F. Zanolin, Second order ordinary differential equations with indefinite weight: the Neumann boundary value problem, Ann. Mat. Pura Appl. (4), 194 (2015), 451-478.
doi: 10.1007/s10231-013-0384-0. |
[12] |
G. Feltrin and F. Zanolin, Existence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems, Adv. Differential Equations, 20 (2015), 937-982. |
[13] |
P. Hess and T. Kato, On some linear and nonlinear eigenvalue problems with an indefinite weight function, Comm. Partial Differential Equations, 5 (1980), 999-1030.
doi: 10.1080/03605308008820162. |
[14] |
J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Applied Mathematical Sciences, 74, Springer-Verlag, New York, 1989.
doi: 10.1007/978-1-4757-2061-7. |
[15] |
P. H. Rabinowitz, Pairs of positive solutions of nonlinear elliptic partial differential equations,, Indiana Univ. Math. J., 23 (): 173.
doi: 10.1512/iumj.1974.23.23014. |
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