과제정보
연구 과제 주관 기관 : National Natural Science Foundation of China, University of Macau
참고문헌
- C.O. Alves, F. S. J. A. Correa, and T. F. Ma, Positive solutions for a quasilinear elliptic equation of Kirchhoff type, Comput. Math. Appl. 49 (2005), no. 1, 85-93. https://doi.org/10.1016/j.camwa.2005.01.008
- A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), no. 4, 349-381. https://doi.org/10.1016/0022-1236(73)90051-7
- A. Arosio and S. Panizzi, On the well-posedness of the Kirchhoff string, Trans. Amer. Math. Soc. 348 (1996), no. 1, 305-330. https://doi.org/10.1090/S0002-9947-96-01532-2
- G. Autuori, F. Colasuonno, P. Pucci, Blow up at infinity of solutions of polyharmonic Kirchhoff systems, Complex Var. Elliptic Equ. 57 (2012), no. 2-4, 379-395. https://doi.org/10.1080/17476933.2011.592584
- G. Autuori, F. Colasuonno, P. Pucci, Lifespan estimates for solutions of polyharmonic Kirchhoff systems, Math. Models Methods Appl. Sci. 22 (2012), no. 2, 1150009, 36 pp.
- G. Autuori, F. Colasuonno, P. Pucci, On the existence of stationary solutions for higher-order p-Kirchhoff problems, Commun. Contemp. Math. 16 (2014), no. 5, 1450002, 43 pp.
- J. V. Baxley, A singular nonlinear boundary value problem: membrane response of a spherical cap, SIAM J. Appl. Math. 48 (1988), no. 3, 497-505. https://doi.org/10.1137/0148028
- G. Bonanno, A critical point theorem via the Ekeland variational principle, Nonlinear Anal. 75 (2012), no. 5, 2992-3007. https://doi.org/10.1016/j.na.2011.12.003
- G. Bonanno, G. Molica Bisci, and V. Radulescu, Weak solutions and energy estimates for a class of nonlinear elliptic Neumann problems, Adv. Nonlinear Stud. 13 (2013), no. 2, 373-389. https://doi.org/10.1515/ans-2013-0207
- H. Brezis and L. Oswald, Remarks on sublinear elliptic equations, Nonlinear Anal. 10 (1986), no. 1, 55-64. https://doi.org/10.1016/0362-546X(86)90011-8
- L. Caffarelli, R. Kohn, and L. Nirenberg, First order interpolation inequalities with weights, Compositio Math. 53 (1984), no. 3, 259-275.
- F. Catrina and Z. Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existstence (and non existstence), and symmetry of extremal functions, Comm. Pure Appl. Math. 54 (2001), no. 2, 229-258. https://doi.org/10.1002/1097-0312(200102)54:2<229::AID-CPA4>3.0.CO;2-I
- M. Chipot and B. Lovat, Some remarks on non local elliptic and parabolic problems, Proceedings of the Second World Congress of Nonlinear Analysts, Part 7 (Athens, 1996). Nonlinear Anal. 30 (1997), no. 7, 4619-4627.
- J. Chu, N. Fan, and P. J. Torres, Periodic solutions for second order singular damped differential equations, J. Math. Anal. Appl. 388 (2012), no. 2, 665-675. https://doi.org/10.1016/j.jmaa.2011.09.061
- J. Chu, S. Heidarkhani, A. Salari, and G. Caristi, Weak solutions and energy estimates for singular p-Laplacian type equations, preprint.
- J. Chu, P. J. Torres, and F. Wang, Twist periodic solutions for differential equations with a combined attractive-repulsive singularity, J. Math. Anal. Appl. 437 (2016), no. 2, 1070-1083. https://doi.org/10.1016/j.jmaa.2016.01.057
- J. Chu, P. J. Torres, and M. Zhang, Periodic solutions of second order non-autonomous singular dynamical systems, J. Differential Equations 239 (2007), no. 1, 196-212. https://doi.org/10.1016/j.jde.2007.05.007
- N. T. Chung and Q. A. Ngo, A multiplicity result for a class of equations of p-Laplacian type with sign-changing nonlinearities, Glasg. Math. J. 51 (2009), no. 3, 513-524. https://doi.org/10.1017/S001708950900514X
- N. T. Chung and H. Q. Toan, Solutions of elliptic problems of p-Laplacian type in a cylindrical symmetric domain, Acta Math. Hungar. 135 (2012), no. 1-2, 42-55. https://doi.org/10.1007/s10474-011-0163-6
- N. T. Chung and H. Q. Toan, Multiple solutions for a class of degenerate nonlocal problems involving sublinear nonlinearities, Matematiche (Catania) 69 (2014), no. 2, 171-182.
- F. Colasuonno and P. Pucci, Multiplicity of solutions for p(x)-polyharmonic elliptic Kirchhoff equations, Nonlinear Anal. 74 (2011), no. 17, 5962-5974. https://doi.org/10.1016/j.na.2011.05.073
- G. D'Agui, Existence results for a mixed boundary value problem with Sturm-Liouville equation, Adv. Pure Appl. Math. 2 (2011), no. 2, 237-248. https://doi.org/10.1515/APAM.2010.043
- D. M. Duc and N. Thanh Vu, Nonuniformly elliptic equations of p-Laplacian type, Nonlinear Anal. 61 (2005), no. 8, 1483-1495. https://doi.org/10.1016/j.na.2005.02.049
- M. Galewski and G. Molica Bisci, Existence results for one-dimensional fractional equations , Math. Methods Appl. Sci. 39 (2016), no. 6, 1480-1492. https://doi.org/10.1002/mma.3582
- J. R. Graef, S. Heidarkhani, and L. Kong, A variational approach to a Kirchhoff-type problem involving two parameters, Results Math. 63 (2013), no. 3-4, 877-889. https://doi.org/10.1007/s00025-012-0238-x
- X. He and W. Zou, Multiple solutions for the Brezis-Nirenberg problem with a Hardy potential and singular coefficients, Comput. Math. Appl. 56 (2008), no. 4, 1025-1031. https://doi.org/10.1016/j.camwa.2008.01.029
- X. He and W. Zou, Infinitely many positive solutions for Kirchhoff-type problems, Nonlinear Anal. 70 (2009), no. 3, 1407-1414. https://doi.org/10.1016/j.na.2008.02.021
- X. He and W. Zou, Multiplicity of solutions for a class of Kirchhoff type problems, Acta Math. Appl. Sin. Engl. Ser. 26 (2010), no. 3, 387-394. https://doi.org/10.1007/s10255-010-0005-2
- S. Heidarkhani, Infinitely many solutions for systems of n two-point Kirchhoff-type boundary value problems, Ann. Polon. Math. 107 (2013), no. 2, 133-152. https://doi.org/10.4064/ap107-2-3
- G. Kirchhoff, Vorlesungen uber mathematische Physik, Mechanik, Teubner, Leipzig, 1883.
- A. Kristaly, H. Lisei, and C. Varga, Multiple solutions for p-Laplacian type equations, Nonlinear Anal. 68 (2008), no. 5, 1375-1381. https://doi.org/10.1016/j.na.2006.12.031
- S.-S. Lin, On the number of positive solutions for nonlinear elliptic equations when a parameter is large, Nonlinear Anal. 16 (1991), no. 3, 283-297. https://doi.org/10.1016/0362-546X(91)90229-T
- J. L. Lions, On some questions in boundary value problems of mathematical physics, Contemporary developments in continuum mechanics and partial differential equations (Proc. Internat. Sympos., Inst. Mat., Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1977), pp. 284-346, North-Holland Math. Stud., 30, North-Holland, Amsterdam-New York, 1978.
- A. Mao and Z. Zhang, Sign-changing and multiple solutions of Kirchhoff-type problems without the P.S. condition, Nonlinear Anal. 70 (2009), no. 3, 1275-1287. https://doi.org/10.1016/j.na.2008.02.011
- G. Molica Bisci and D. Repovs, Nonlinear Neumann problems driven by a nonhomogeneous differential operator, Bull. Math. Soc. Sci. Math. Roumanie Tome 57(105) (2014), no. 1, 13-25.
- D. Motreanu and V. Radulescu, Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems, Nonconvex Optimization and Applications, Kluwer Academic Publishers, 2003.
- K. Perera and Z. T. Zhang, Nontrivial solutions of Kirchhoff-type problems via the Yang index, J. Differential Equations 221 (2006), no. 1, 246-255. https://doi.org/10.1016/j.jde.2005.03.006
- P. Pucci and J. Serrin, A mountain pass theorem, J. Differential Equations 60 (1985), no. 1, 142-149. https://doi.org/10.1016/0022-0396(85)90125-1
- P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics, 65. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1986.
- B. Ricceri, On an elliptic Kirchhoff-type problem depending on two parameters, J. Global Optim. 46 (2010), no. 4, 543-549. https://doi.org/10.1007/s10898-009-9438-7
- J. Tyagi, Existence of nontrivial solutions for singular quasilinear equations with sign changing nonlinearity, Electron. J. Differential Equations 2010 (2010), no. 117, 9 pp.
- B. Xuan, The eigenvalue problem for a singular quasilinear elliptic equation, Electron. J. Differential Equations 2004 (2004), no. 16, 11 pp.
- Z. Yang, D. Geng, and H. Yan, Three solutions for singular p-Laplacian type equations, Electron. J. Differential Equations 2008 (2008), no. 61, 12 pp.