Abstract
In this paper, we discuss the jumping nonlinearity problem the special case where f = 0 and problems which behave asymptotically like (1).
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References
N. Arouszajn, A. Krzywicki and I. Szarski, “A unique continuation theorem for exterior differential forms on Riemannian manifolds”, Ark. Math. 4 (1962), 417–453.
M. D’Aujourd’hui, “Sur l’ensemble de résonance d’un problème demi-linéaire”, preprint, EPFL, Lausanne.
L. Caffarelli and A. Friedman, “Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations”, J. Diff. Eqns. 60 (1985), 420–433.
H. Cartan, Calcul Différentiel, Hermann, Paris, 1967.
K.C. Chang, Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston, 1993.
X.Y. Chen, “Polynomial asymptotics near zero points of solutions of general elliptic equations”, preprint.
E.N. Dancer, “On the Dirichlet problem for weakly non-linear elliptic partial differential equations”, Proc. Royal Soc. Edinburgh 76A (1977), 283–300.
E.N. Dancer, “On the existence of solutions of certain asymptotically homogeneous problems”, Math. Z. 177 (1981), 33–48.
E.N. Dancer, “Multiple solutions of asymptotically homogeneous problems”, Annali di Matematica Pura ed Applicada 152 (1988), 63–78.
E.N. Dancer, “Degenerate critical points, homotopy indices and Morse inequalities”, J. Reine Ang. Math. 350 (1984), 1–22.
E.N. Dancer, “Degenerate critical points, homotopy indices and Morse inequalities II”, J. Reine Ang. Math 382 (1987), 145–164.
E.N. Dancer, “On positive solutions of some pairs of differential equations II”, J. Diff. Eqns. 60 (1985), 236–258.
E.N. Dancer, “Generic domain dependence for non-smooth equations and the open set problem for jumping nonlinearities”, Topological Methods in Nonlinear Analysis 1 (1993), 139–150.
E.N. Dancer, “On the effect of domain shape on the number of positive solutions of certain nonlinear equations II”, J. Diff. Eqns. 87 (1990), 316–339.
D.G. de Figueredo and J. Gossez, “On the first curve of the Fucik spectrum of an elliptic operator”, Diff. and Integral Eqns. 7 (1994), 1285–1302.
A. Dold, Algebraic Topology, Springer-Verlag, Berlin, 1970.
S. Fucik, Solvability of Nonlinear Equations and Boundary Value Problems, Reidel, Dordrecht, 1980.
C. Magalhaes, “Semilinear elliptic problem with crossing of multiple eigenvalues”, Comm. Partial Diff. Eqns. 15 (1990), 1265–1292.
A Marino, A. Micheletti and A. Pistoia, “A non symmetric asymptotically linear problem”, Topological methods in nonlinear analysis 4 (1994), 289–339.
A Micheletti and A. Pistoia, “A note on the resonance set for a semilinear elliptic equation and an application to jumping nonlinearities”, Topological methods in nonlinear analysis 6 (1995), 67–80.
A. Pistoia, “A generic property of the resonance set of an elliptic operator with respect to the domain”, to appear in Proc. Royal Soc. Edinburgh.
P. Pope, Solvability of Non Self-adjoint and Higher Order Differential Equations with Jumping Nonlinearities, Ph.D. thesis, University of New England, 1984.
J. Rauch and M. Taylor, “Potential and scattering theory in wildly perturbed domains”, J. Funct. Anal. 18 (1975), 27–59.
K.J. Rybakowski, The Homotopy Index and Partial Differential Equations, Springer-Verlag, Berlin, 1987.
J. Saut and R. Temam, “Generic properties of nonlinear boundary value problems”, Comm. Partial Diff. Eqns. 4 (1979), 293–319.
M. Schechter, “The Fucik spectrum”, Indiana University Math J. 43 (1994), 1139–1157.
S. Solimini, “Some remarks on the number of solutions of some nonlinear elliptic problems”, Analyse Nonlinéaire 2 (1985), 143–156.
F. Stummel, Perturbation of Domains in Elliptic Boundary Value Problems, in Lecture Notes in Mathematics 503, 110–135, Springer-Verlag, Berlin, 1975.
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Dancer, E.N. (1999). Remarks on Jumping Nonlinearities. In: Escher, J., Simonett, G. (eds) Topics in Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 35. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8765-6_7
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DOI: https://doi.org/10.1007/978-3-0348-8765-6_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9764-8
Online ISBN: 978-3-0348-8765-6
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