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On semilinear elliptic equations with indefinite nonlinearities. (English) Zbl 0809.35022
Summary: This paper concerns semilinear elliptic equations whose nonlinear term has the form $$W(x) f(u)$$ where $$W$$ changes sign. We study the existence of positive solutions and their multiplicity. The important role played by the negative part of $$W$$ is contained in a condition which is shown to be necessary for homogeneous $$f$$. More general existence questions are also discussed.

##### MSC:
 35J65 Nonlinear boundary value problems for linear elliptic equations 35B32 Bifurcations in context of PDEs 35J20 Variational methods for second-order elliptic equations 35J25 Boundary value problems for second-order elliptic equations 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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