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.
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 
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
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[1] A. Ambrosetti G. Mancini: Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance. The case of the simple eigenvalue. Journal of Diff. Eq., vol. 28, (1978), 220-245. | DOI | MR

[2] S. Fučík: Remarks on a result by A. Ambrosetti and G. Prodi. U.M.I., (4), 11 (1975), 259-267. | MR

[3] M. A. Krasnoselskij: Topological methods in the theory of nonlinear integral equations. Pergamon Press, London, 1964.

[4] J. Minty: Monotone operators in Hilbert space. Duke Math. Journal 29 (1962), 341 - 346. | DOI | MR

[5] A. N. Kolmogorov S. V. Fomin: Элементы теории функций и функционального анализа. Nauka, Moskva, 1972.

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