과제정보
This work was financially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (NRF-2020R1F1A1A01065912).
참고문헌
- H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. 18 (1976), no. 4, 620- 709. https://doi.org/10.1137/1018114
- T. Bartsch and Z.-Q. Wang, Sign changing solutions of nonlinear Schrodinger equations, Topol. Methods Nonlinear Anal. 13 (1999), no. 2, 191-198. https://doi.org/10.12775/TMNA.1999.010
- K.J. Brown, M.M.A. Ibrahim and R. Shivaji, S - shaped bifurcation curves, Nonlinear Analysis, 5 (1981), 475-486. https://doi.org/10.1016/0362-546X(81)90096-1
- D. Butler, E. Ko, E. Lee and R. Shivaji, Positive radial solutions for elliptic equations on exterior domains with nonlinear boundary conditions, Commun. Pure Appl. Anal. 13 (2014), no. 6, 2713-2731. https://doi.org/10.3934/cpaa.2014.13.2713
- D. Butler, S. Sasi and R. Shivaji, Existence of alternate steady states in a phosphorous cycling model, ISRN Math. Anal. 2012, Art. ID 869147, 11 pp.
- S. R. Carpenter, D. Ludwig and W. A. Brock, Management of eutrophication for lakes subject to potentially irreversible change, Ecological Applications, vol. 9, (1999), no 3, pp. 751-771. https://doi.org/10.1890/1051-0761(1999)009[0751:MOEFLS]2.0.CO;2
- M. Cuesta, Q. Ramos and Humberto, A weighted eigenvalue problem for the p-Laplacian plus a potential, NoDEA Nonlinear Differential Equations Appl. 16 (2009), no. 4, 469-491. https://doi.org/10.1007/s00030-009-0026-9
- S. Cui, Existence and nonexistence of positive solutions for singular semilinear elliptic boundary value problems, Nonlinear Analysis, 41 (2001), pp.149- 176. https://doi.org/10.1016/S0362-546X(98)00271-5
- R. Dhanya, E. Ko, R. Shivaji, A three solution theorem for singular nonlinear elliptic boundary value problems, J. Math. Anal. Appl. 424 (2015), no. 1, 598-612. https://doi.org/10.1016/j.jmaa.2014.11.012
- G.M. Figueiredo, J.R. Santos Junior and A. Suarez, Structure of the set of positive solutions of a non-linear Schrodinger equation, (English summary) Israel J. Math. 227 (2018), no. 1, 485-505. https://doi.org/10.1007/s11856-018-1752-7
- J. Fleckinger, J. Hernandez and F. de Thelin, Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 7 (2004), no. 1, 159-188.
- J. Giacomoni, I.Schindler and P. Takac, Sobolev versus Holder local minimizers and existence of multiple solutions for a singular quasilinear equation, Ann. Scuola Norm. Suo. Pisa Cl. Sci. (5) Vol. VI (2007), 117-158. https://doi.org/10.2422/2036-2145.2007.1.07
- Y. Guo, Z.-Q. Wang, X. Zeng and H.-S. Zhou, Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials, Nonlinearity, 31 (2018), no. 3, 957-979. https://doi.org/10.1088/1361-6544/aa99a8
- E. Ko, Multiplicity of positive solutions of elliptic equations with falling zeros, preprinted.
- E. Ko, E.K. Lee and R. Shivaji, Multiplicity results for classes of infinite positone problems, Z. Anal. Anwend. 30 (2011), no. 3, 305-318. https://doi.org/10.4171/zaa/1436
- E. Ko, E.K. Lee and R. Shivaji, Multiplicity results for classes of singular problems on an exterior domain, Discrete Contin. Dyn. Syst. 33 (2013), no. 11-12, 5153-5166. https://doi.org/10.3934/dcds.2013.33.5153
- E. Ko, E.K. Lee and R. Shivaji, Multiplicity of positive solutions to a class of Schrodinger-type singular problems, preprinted.
- E. Lee, S. Sasi and R. Shivaji, An ecological model with a Σ-shaped bifurcation curve, Nonlinear Anal. Real World Appl. 13 (2012), no. 2, 634-642. https://doi.org/10.1016/j.nonrwa.2011.07.054
- J. Q. Liu, Y. Q. Wang and Z.-Q. Wang, Solutions for quasilinear Schrodinger equations via the Nehari method, Comm. Partial Differential Equations 29 (2004), no. 5-6, 879-901. https://doi.org/10.1081/PDE-120037335
- J. Lopez-Gomez, The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems, J. Differential Equations, 127 (1996), no. 1, 263-294. https://doi.org/10.1006/jdeq.1996.0070
- P.H. Rabinowitz, On a class of nonlinear Schrodinger equations, Z. Angew. Math. Phys. 43 (1992), no. 2, 270-291. https://doi.org/10.1007/BF00946631
- M. Ramaswamy and R. Shivaji, Multiple positive solutions for classes of p-laplacian equations, Differential Integral Equations, 17 (2004), no. 11-12, 1255 - 1261.