The multiplicity of solutions and geometry of a nonlinear elliptic equation

Studia Mathematica

Volumn 120, Issue 3, 1996, Pages 259-270

  Choi, Q Heung ^a   Chun, Sungki ^a   Jung, Tacksun ^b  

^a Inha University   (South Korea)

^b Kunsan National University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000904765     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm-120-3-259-270     Document Type: Article

References (15)

1. H. A mann and P. Hess, A multiplicity result for a class of elliptic boundary value problems, Proc. Roy. Soc. Edinburgh 84 (1979), 145-151.
2. A. Ambrosetti and G. Prodi, A Primer of Nonlinear Analysis, Cambridge Stud. Adv. Math. 34, Cambridge University Press, 1993.
3. Q. H. Choi and T. Jung, Multiplicity of solutions of nonlinear wave equations with nonlinearities crossing eigenvalues, Hokkaido Math. J. 24 (1995), 53-62.
4. _, _, An application of a variatiorial reduction method to a nonlinear wave equation, J. Differential Equations 117 (1995), 390-410.
5. J. M. Coron, Periodic solutions of a nonlinear wave equation without assumptions of monotonicity, Math. Ann. 262 (1983), 273-285.
6. E. N. Dancer, On the ranges of certain weakly nonlinear elliptic partial differential equations, J. Math. Pures Appl. 57 (1978), 351-366.
7. A. C. Lazer and P. J. McKenna, Existence, uniqueness, and stability of oscillations in differential equations with symmetric nonlinearities, Trans. Amer. Math. Soc. 315 (1989), 721-739.
8. _, _, Some multiplicity results for a class of semilinear elliptic and parabolic boundary value problems, J. Math. Anal. Appl. 107 (1985), 371-395.
9. _, _, A symmetry theorem and applications to nonlinear partial differential equations, J. Differential Equations 72 (1988), 95-106.
10. P. J. McKenna, Topological Methods for Asymmetric Boundary Value Problems. Lecture Notes Ser. 11, Res. Inst. Math., Global Analysis Res. Center. Seoul National University, 1993.
11. P. J. McKenna, R. Redlinger and W. Walter, Multiplicity results for asymptotically homogeneous semilinear boundary value problems, Ann. Mat. Pura Appl. (4) 143 (1986), 347-257.
12. P. J. McKenna and W. Walter, On the multiplicity of the solution set of some nonlinear boundary value problems, Nonlinear Anal. 8 (1984), 893-907.
13. K. Schmitt, Boundary value problems with jumping nonlinearities, Rocky Mountain J. Math. 16 (1986), 481-496.
14. J. Schröder, Operator Inequalities, Academic Press, New York, 1980.
15. S. Solimini, Some remarks on the number of solutions of some nonlinear elliptic problems, Ann. Inst. H. Poincaré 2 (1985), 143-156.