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Zbl 1149.35044
de Paiva, Francisco Odair; Massa, Eugenio
Semilinear elliptic problems near resonance with a nonprincipal eigenvalue.
(English)
[J] J. Math. Anal. Appl. 342, No. 1, 638-650 (2008). ISSN 0022-247X

Summary: We consider the Dirichlet problem for the equation $-\Delta u=\lambda u\pm f(x,u)+h(x)$ in a bounded domain, where $f$ has a sublinear growth and $h\in L^2$. We find suitable conditions on $f$ and $h$ in order to have at least two solutions for $\lambda$ near to an eigenvalue of $-\Delta$. A typical example to which our results apply is when $f(x,u)$ behaves at infinity like $a(x)|u|^{q-2}u$, with $M>a(x)>\delta>0$, and $1<q<2$.
MSC 2000:
*35J65 (Nonlinear) BVP for (non)linear elliptic equations
35P05 General spectral theory of PDE
58J50 Spectral problems; spectral geometry; scattering theory

Keywords: semilinear elliptic equations; multiplicity of solutions; quasi resonant problems; saddle point geometry

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