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Zbl 0731.35036
Bahri, Abbas; Li, Yan Yan
On a min-max procedure for the existence of a positive solution for certain scalar field equations in ${\bbfR}\sp N$.
(English)
[J] Rev. Mat. Iberoam. 6, No.1-2, 1-15 (1990). ISSN 0213-2230

The problem of the existence of positive solutions $u\in H\sp 1({\bbfR}\sp n)$ of the semilinear elliptic equation $$-\Delta u+u- q(x)\vert u\vert\sp{p-1}u=0$$ is considered. Under suitable conditions on p,n and $q(x)\in L\sp{\infty}({\bbfR}\sp n)$ a min-max procedure for the corresponding variational functional J which is based on topological methods shows the existence of at least one positive solution.
[H.Schmitz (Heidelberg)]
MSC 2000:
*35J65 (Nonlinear) BVP for (non)linear elliptic equations
47H11 Degree theory
58E05 Abstract critical point theory

Keywords: positive solutions; semilinear elliptic equation

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