1.

A. K. Ben-Naoum, C. Fabry and D. Smets, Structure of the Fučik spectrum and existence of solutions for equations with asymmetric nonlinearity , Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), 241–265 \ref \key 2 MR1830411 10.1017/S030821050000086XA. K. Ben-Naoum, C. Fabry and D. Smets, Structure of the Fučik spectrum and existence of solutions for equations with asymmetric nonlinearity , Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), 241–265 \ref \key 2 MR1830411 10.1017/S030821050000086X

2.

G. Bredon, An Introduction to Compact Transformation Groups, Academic Press, New York (1972) \ref \key 3 MR413144G. Bredon, An Introduction to Compact Transformation Groups, Academic Press, New York (1972) \ref \key 3 MR413144

3.

K. C. Chang, Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston (1993) \ref \key 4 MR1196690K. C. Chang, Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston (1993) \ref \key 4 MR1196690

4.

E. N. Dancer, Remarks on jumping nonlinearities , 101–115, Topics in Nonlinear Analysis (Escher and Simonett, eds.), Birkhäuser, Basel (1999) \ref \key 5 ––––, On the Dirichlet problem for weakly nonlinear elliptic partial differential equations , Proc. Roy. Soc. Edinburgh Sect. A, 76 (1977), 283–300 \ref \key 6––––, Generic domain dependence and the open set problem for jumping nonlinearities , Topol. Methods Nonlinear Anal., 1 (1993), 139–150 \ref \key 7––––, Degenerate critical points, homotopy indices and Morse inequalities , J. Reine Angew. Math., 350 (1984), 1–22 \ref \key 8––––, Degenerate critical points, homotopy indices and Morse inequalities \romII, J. Reine Angew. Math., 382 (1987), 145–164 \ref \key 9––––, On the effect of domain in shape on the number of positive solutions of certain nonlinear equations , J. Differential Equations, 74 (1988), 120–156 \ref \key 10––––, Multiple solutions of asymptotically homogeneous problems , Ann. Mat. Pura Appl., 152 (1988), 63–78 \ref \key 11––––, Dynamics of Lotka–Volterra competition systems with large interaction \romII. in preparation \ref \key 12 MR1725568 10.1007/978-3-0348-8765-6_7E. N. Dancer, Remarks on jumping nonlinearities , 101–115, Topics in Nonlinear Analysis (Escher and Simonett, eds.), Birkhäuser, Basel (1999) \ref \key 5 ––––, On the Dirichlet problem for weakly nonlinear elliptic partial differential equations , Proc. Roy. Soc. Edinburgh Sect. A, 76 (1977), 283–300 \ref \key 6––––, Generic domain dependence and the open set problem for jumping nonlinearities , Topol. Methods Nonlinear Anal., 1 (1993), 139–150 \ref \key 7––––, Degenerate critical points, homotopy indices and Morse inequalities , J. Reine Angew. Math., 350 (1984), 1–22 \ref \key 8––––, Degenerate critical points, homotopy indices and Morse inequalities \romII, J. Reine Angew. Math., 382 (1987), 145–164 \ref \key 9––––, On the effect of domain in shape on the number of positive solutions of certain nonlinear equations , J. Differential Equations, 74 (1988), 120–156 \ref \key 10––––, Multiple solutions of asymptotically homogeneous problems , Ann. Mat. Pura Appl., 152 (1988), 63–78 \ref \key 11––––, Dynamics of Lotka–Volterra competition systems with large interaction \romII. in preparation \ref \key 12 MR1725568 10.1007/978-3-0348-8765-6_7

5.

E. N. Dancer and S. Yan, Effect of the domain geometry on the existence of multipeak solutions for an elliptic problem , Topol. Methods Nonlinear Anal., 14 (1999), 1–38 \ref \key 13 MR1758878E. N. Dancer and S. Yan, Effect of the domain geometry on the existence of multipeak solutions for an elliptic problem , Topol. Methods Nonlinear Anal., 14 (1999), 1–38 \ref \key 13 MR1758878

6.

A. Dold, Algebraic Topology, Springer–Verlag, Berlin (1970) \ref \key 14A. Dold, Algebraic Topology, Springer–Verlag, Berlin (1970) \ref \key 14

7.

Th. Gallouet and O. Kavian, Resonance for jumping nonlinearities, Comm. Partial Differential Equations, 7 (1982), 325–342  MR646710 10.1080/03605308208820225Th. Gallouet and O. Kavian, Resonance for jumping nonlinearities, Comm. Partial Differential Equations, 7 (1982), 325–342  MR646710 10.1080/03605308208820225

8.

\ref \key 15G. Katriel, Uniqueness of periodic solutions for asymptotically linear Duffing equations with strong damping, Topol. Methods Nonlinear Anal., 12 (1998), 263–274 \ref \key 16 MR1701263\ref \key 15G. Katriel, Uniqueness of periodic solutions for asymptotically linear Duffing equations with strong damping, Topol. Methods Nonlinear Anal., 12 (1998), 263–274 \ref \key 16 MR1701263

9.

C. Magaelhaes, Semilinear elliptic problems with crossing of multiple eigenvalues , Comm. Partial Differential Equations, 15 (1990), 1265–1292  MR1077275 10.1080/03605309908820724C. Magaelhaes, Semilinear elliptic problems with crossing of multiple eigenvalues , Comm. Partial Differential Equations, 15 (1990), 1265–1292  MR1077275 10.1080/03605309908820724

10.

\ref \key 17C. Margulies and W. Margulies, An example of the Fučik spectrum, Nonlinear Anal., 29 (1997), 1373–1378  MR1484910\ref \key 17C. Margulies and W. Margulies, An example of the Fučik spectrum, Nonlinear Anal., 29 (1997), 1373–1378  MR1484910

11.

\ref \key 18A. Marino, A. Micheletti and A. Pistoia, A non symmetric asymptotically linear problem , Topol. Methods Nonlinear Anal., 4 (1994) \ref \key 18A. Marino, A. Micheletti and A. Pistoia, A non symmetric asymptotically linear problem , Topol. Methods Nonlinear Anal., 4 (1994)

12.

\ref \key 19W. Massey, Homology and Cohomology Theory, Marcel Dekker, Basel (1978)  MR488016\ref \key 19W. Massey, Homology and Cohomology Theory, Marcel Dekker, Basel (1978)  MR488016

13.

\ref \key 20A. Micheletti, Perturbazione dello spectro dell operatore di Laplace in relazione ad una variazione del campo , Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 26 (1972), 151–169  MR367480\ref \key 20A. Micheletti, Perturbazione dello spectro dell operatore di Laplace in relazione ad una variazione del campo , Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 26 (1972), 151–169  MR367480

14.

\ref \key 21K. Perera and M. Schechter, The Fučik spectrum and critical groups, Proc. Amer. Math. Soc., 129 (2001), 2301–2308 \ref \key 22 MR1823913 10.1090/S0002-9939-01-05968-8\ref \key 21K. Perera and M. Schechter, The Fučik spectrum and critical groups, Proc. Amer. Math. Soc., 129 (2001), 2301–2308 \ref \key 22 MR1823913 10.1090/S0002-9939-01-05968-8

15.

A. Pistoia, A generic property of the resonance set of an elliptic operator with respect to the domain , Proc. Roy. Soc. Edinburgh Sect. A, 127 (1997), 1301–1310 \ref \key 23 MR1489437 10.1017/S0308210500027062A. Pistoia, A generic property of the resonance set of an elliptic operator with respect to the domain , Proc. Roy. Soc. Edinburgh Sect. A, 127 (1997), 1301–1310 \ref \key 23 MR1489437 10.1017/S0308210500027062

16.

P. Pope, Solvability of non self-adjoint and higher order differential equations with jumping nonlinearities , Ph. D. thesis, University of New England(1984) P. Pope, Solvability of non self-adjoint and higher order differential equations with jumping nonlinearities , Ph. D. thesis, University of New England(1984)

17.

\ref \key 24K. Rybakowski, The Homotopy Index and Partial Differential Equations, Springer–Verlag, Berlin (1987) \ref \key 25 MR910097\ref \key 24K. Rybakowski, The Homotopy Index and Partial Differential Equations, Springer–Verlag, Berlin (1987) \ref \key 25 MR910097

18.

B. Rynne, Generic properties of the Fučik spectrum of elliptic operators , Proc. Roy. Soc. Edinburgh Sect. A, 130 (2000), 217–224  MR1742587 10.1017/S0308210500000111B. Rynne, Generic properties of the Fučik spectrum of elliptic operators , Proc. Roy. Soc. Edinburgh Sect. A, 130 (2000), 217–224  MR1742587 10.1017/S0308210500000111

19.

\ref \key 26M. Schechter, The Fučik Spectrum, Indiana Univ. Math. J., 43 (1994), 1139–1157  MR1322614 10.1512/iumj.1994.43.43050\ref \key 26M. Schechter, The Fučik Spectrum, Indiana Univ. Math. J., 43 (1994), 1139–1157  MR1322614 10.1512/iumj.1994.43.43050

20.

\ref \key 27E. Spanier, Algebraic Topology, McGraw Hill, New York (1966) \ref \key 28 MR210112\ref \key 27E. Spanier, Algebraic Topology, McGraw Hill, New York (1966) \ref \key 28 MR210112

21.

K. Uhlenbeck, Generic properties of eigenfunctions, Amer. J. Math., 98 (1976), 1059–1078  MR464332 10.2307/2374041K. Uhlenbeck, Generic properties of eigenfunctions, Amer. J. Math., 98 (1976), 1059–1078  MR464332 10.2307/2374041