Summary
We consider the solvability of some nonlinear boundary value problems for differential equations where the nonlinearity is bounded. This involves the study of the asymptotic behaviour of certain multivalued functionals.
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References
J. C.Alexander,A primer on connectivity, preprint.
H.Bohr,Almost periodic functions, Chelsea, New York (1966).
A. Castro,Periodic solutions of the forced pendulum equation, inDifferential Equations, edited by S. Ahmad, M. Keener and A. Lazer, Academic Press, New York (1980).
E. Copson,Asymptotic expansions, Cambridge Univ. Press, Cambridge (1965).
E. N. Dancer,Asymptotics applied to nonlinear boundary-value problems, Bull. Austral. Math. Soc.,18 (1978), pp. 29–35.
E. N. Dancer,On the existence of solutions of certain asymptotically homogeneous problems, Math. Zeit.,177 (1981), pp. 33–48.
E. N. Dancer,On the ranges of certain weakly nonlinear elliptic partial differential equations, J. Math. Pure et Appl.,57 (1978), pp. 351–366.
E. N. Dancer,On the Dirichlet problem for weakly nonlinear elliptic partial differential equations, Proc. Royal Soc. Edinburgh,76 A (1977), pp. 283–300.
E. N. Dancer,Global solution branches for positive mappings, Archives Rat. Mech. Anal.,52 (1973), pp. 181–192.
P.Drabek,Solvability of nonlinear problems at resonance, to appear.
A. Erdelyi,Asymptotic expansions, Dover, New York (1956).
H. Federer,Geometric measure theory, Springer-Verlag, Berlin (1969).
S. Fucik,Nonlinear noncoercive problems, inSurvey on theoretical and numerical trends in nonlinear analysis, Conf. Sem. Mat. Univ. Bari, no. 163–168, Editori Laterza, Bari (1980).
S. Fucik,Solvability of nonlinear equations and boundary-value problems, Reidel, Dordrecht (1980).
S.Fucik,Open problems in the solvability of nonlinear equations, Lecture at the Oberwolfach Conference on Nonlinear Functional Analysis, January 1976.
D. Gromoll -W. Meyer,On differentiale functions with isolated critical points, Topology,8 (1969), pp. 361–369.
P. Hess,A remark on a preceding paper of Fucik and Krbec, Math. Zeit.,155 (1977), pp. 139–141.
N. Kuiper, C1-equivalenceof functions near isolated critical points, in Symposium on Infinite Dimensional Topology, edited by R. Anderson, Princeton University Press, Princeton (1972).
V. Maslov,Theorie des perturbations ei méthodes asymptotiques, Dunod, Paris (1972).
P. H. Rabinowitz,Some global results for nonlinear eigenvalue problems, J. Functional Anal.,7 (1971), pp. 487–513.
P. H. Rabinowitz,A bifurcation theorem for potential operators, J. Functional Anal.,25 (1977), pp. 412–424.
P. H. Rabinowitz,Nonlinear Sturm-Liouville problems for second order differential equations, Comm. Pure Appl. Math.,23 (1970), pp. 936–961.
R. Turner,Transversality and cone maps, Arch. Rat. Mech. Anal.,58 (1975), pp. 151–179.
K. Uhlenbeck,Generic properties of eigenf'unctions, Amer. Journ. Math.,98 (1976), pp. 1059–1078.
L. Ward,Topology, Marcel Dekker, New York (1972).
G. Whyburn,Topological analysis, Princeton University Press, Princeton (1958).
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Dancer, E.N. On the use of asymptotics in nonlinear boundary value problems. Annali di Matematica pura ed applicata 131, 167–185 (1982). https://doi.org/10.1007/BF01765151
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DOI: https://doi.org/10.1007/BF01765151