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Remarks on nonlinear noncoercive problems with jumping nonlinearities. (English) Zbl 0557.47032
This paper deals with equations of the type \[ (1)\quad J(x)-\mu S(x^+)+\nu S(x^-)+G(x)=f, \] which were studied in the principal Fučík’s works; the survey of the results in this direction up to 1980 is given in the book of S. Fučík: ”Solvability of nonlinear equations and boundary value problems” (1980; Zbl 0453.47035). Our aim was to give a short survey of the results in this field which have been published during the last five years and which are not contained in Fučík’s book mentioned above. We formulate also some open problems the solutions of which could lead to a better understanding of the equations of the type (1).
MSC:
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
34B15 Nonlinear boundary value problems for ordinary differential equations
34L99 Ordinary differential operators
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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