American Institute of Mathematical Sciences

July  1999, 5(3): 489-493. doi: 10.3934/dcds.1999.5.489

Multiple solutions theorems for semilinear elliptic boundary value problems with resonance at infinity

 1 Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China 2 Institute of Mathematics, Academia Sinica, Beijing, 100080, China

Received  August 1998 Revised  February 1999 Published  May 1999

In this paper, we use Lyapunov-Schmidt method and Morse theory to study semilinear elliptic boundary value problems with resonance at infinity, and get new multiple solutions theorems.
Citation: Shujie Li, Zhitao Zhang. Multiple solutions theorems for semilinear elliptic boundary value problems with resonance at infinity. Discrete & Continuous Dynamical Systems, 1999, 5 (3) : 489-493. doi: 10.3934/dcds.1999.5.489
 [1] Sergiu Aizicovici, Nikolaos S. Papageorgiou, Vasile Staicu. Nonlinear Dirichlet problems with double resonance. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1147-1168. doi: 10.3934/cpaa.2017056 [2] Nikolaos S. Papageorgiou, Calogero Vetro, Francesca Vetro. Multiple solutions for (p, 2)-equations at resonance. Discrete & Continuous Dynamical Systems - S, 2019, 12 (2) : 347-374. doi: 10.3934/dcdss.2019024 [3] Philip Korman. Curves of equiharmonic solutions, and problems at resonance. Discrete & Continuous Dynamical Systems, 2014, 34 (7) : 2847-2860. doi: 10.3934/dcds.2014.34.2847 [4] Shouchuan Hu, Nikolaos S. Papageorgiou. Double resonance for Dirichlet problems with unbounded indefinite potential and combined nonlinearities. Communications on Pure & Applied Analysis, 2012, 11 (5) : 2005-2021. doi: 10.3934/cpaa.2012.11.2005 [5] Laura Olian Fannio. Multiple periodic solutions of Hamiltonian systems with strong resonance at infinity. Discrete & Continuous Dynamical Systems, 1997, 3 (2) : 251-264. doi: 10.3934/dcds.1997.3.251 [6] Wenming Zou. Multiple solutions results for two-point boundary value problem with resonance. Discrete & Continuous Dynamical Systems, 1998, 4 (3) : 485-496. doi: 10.3934/dcds.1998.4.485 [7] Leszek Gasiński, Nikolaos S. Papageorgiou. Dirichlet $(p,q)$-equations at resonance. Discrete & Continuous Dynamical Systems, 2014, 34 (5) : 2037-2060. doi: 10.3934/dcds.2014.34.2037 [8] Roberta Filippucci, Chiara Lini. Existence of solutions for quasilinear Dirichlet problems with gradient terms. Discrete & Continuous Dynamical Systems - S, 2019, 12 (2) : 267-286. doi: 10.3934/dcdss.2019019 [9] Alfonso Castro, Jorge Cossio, Carlos Vélez. Existence and qualitative properties of solutions for nonlinear Dirichlet problems. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 123-140. doi: 10.3934/dcds.2013.33.123 [10] Shouchuan Hu, Nikolaos S. Papageorgiou. Solutions of nonlinear nonhomogeneous Neumann and Dirichlet problems. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2889-2922. doi: 10.3934/cpaa.2013.12.2889 [11] Tadeusz Kulczycki, Robert Stańczy. Multiple solutions for Dirichlet nonlinear BVPs involving fractional Laplacian. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2581-2591. doi: 10.3934/dcdsb.2014.19.2581 [12] Francisco Odair de Paiva. Multiple solutions for a class of quasilinear problems. Discrete & Continuous Dynamical Systems, 2006, 15 (2) : 669-680. doi: 10.3934/dcds.2006.15.669 [13] Shu-Zhi Song, Shang-Jie Chen, Chun-Lei Tang. Existence of solutions for Kirchhoff type problems with resonance at higher eigenvalues. Discrete & Continuous Dynamical Systems, 2016, 36 (11) : 6453-6473. doi: 10.3934/dcds.2016078 [14] Jiafeng Liao, Peng Zhang, Jiu Liu, Chunlei Tang. Existence and multiplicity of positive solutions for a class of Kirchhoff type problems at resonance. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1959-1974. doi: 10.3934/dcdss.2016080 [15] Sophia Th. Kyritsi, Nikolaos S. Papageorgiou. Multiple solutions for nonlinear coercive Neumann problems. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1957-1974. doi: 10.3934/cpaa.2009.8.1957 [16] Xing Liu, Yijing Sun. Multiple positive solutions for Kirchhoff type problems with singularity. Communications on Pure & Applied Analysis, 2013, 12 (2) : 721-733. doi: 10.3934/cpaa.2013.12.721 [17] John V. Baxley, Philip T. Carroll. Nonlinear boundary value problems with multiple positive solutions. Conference Publications, 2003, 2003 (Special) : 83-90. doi: 10.3934/proc.2003.2003.83 [18] Monica Musso, Donato Passaseo. Multiple solutions of Neumann elliptic problems with critical nonlinearity. Discrete & Continuous Dynamical Systems, 1999, 5 (2) : 301-320. doi: 10.3934/dcds.1999.5.301 [19] Leszek Gasiński, Nikolaos S. Papageorgiou. Multiple solutions for a class of nonlinear Neumann eigenvalue problems. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1491-1512. doi: 10.3934/cpaa.2014.13.1491 [20] Diego Averna, Nikolaos S. Papageorgiou, Elisabetta Tornatore. Multiple solutions for nonlinear nonhomogeneous resonant coercive problems. Discrete & Continuous Dynamical Systems - S, 2018, 11 (2) : 155-178. doi: 10.3934/dcdss.2018010

2020 Impact Factor: 1.392