Geodesic
Nonlinear elliptic problems with jumping nonlinearities near the first eigenvalue
Applications of Mathematics, Tome 26 (1981) no. 4, pp. 304-311.

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In this paper existence and multiplicity of solutions of the elliptic problem $\Cal L u + \lambda_1u+\mu u^+vu^-+g(x,u)=f$ in $\Omega$ $Bu=0$ on $\partial\Omega$, are discussed provided the parameters $\mu$ and $v$ are close to the first eigenvalue $\lamda_1$. The sufficient conditions presented here are more general than those in given by S. Fučík in his aerlier paper.
DOI : 10.21136/AM.1981.103919
Classification : 35J60, 47J05, 73C50
Keywords: multiplicity of solutions; weakly nonlinear elliptic equations 
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     title = {Nonlinear elliptic problems with jumping nonlinearities near the first eigenvalue},
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Drábek, Pavel. Nonlinear elliptic problems with jumping nonlinearities near the first eigenvalue. Applications of Mathematics, Tome 26 (1981) no. 4, pp. 304-311. doi : 10.21136/AM.1981.103919. http://geodesic.mathdoc.fr/articles/10.21136/AM.1981.103919/

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