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Existence results for some fourth-order nonlinear elliptic problems of local superlinearity and sublinearity. (English) Zbl 1146.35362
Summary: In this paper we study the existence of positive solutions for the problem $\Delta^2u+c\Delta u=f(x,u) \text{ in }\Omega, u\geq 0, u\not\equiv 0\text{ in }\Omega, u=\Delta u=0 \text{ on }\partial\Omega$ where $$c<\lambda_1(\Omega)$$ and $$f(x,u)$$ satisfies the local superlinearity and sublinearity condition.

##### MSC:
 35J60 Nonlinear elliptic equations 35J35 Variational methods for higher-order elliptic equations 35J40 Boundary value problems for higher-order elliptic equations 47J30 Variational methods involving nonlinear operators
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##### References:
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