Differential and Integral Equations

On the Fučí k spectrum for the $p$-Laplacian

Anna Maria Micheletti and Angela Pistoia

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We prove that the set $\big\{(\alpha,\beta)\in\mathbb R^2 : $ the problem $-\Delta_pu=\alpha (u^+)^{p-1}-\beta (u^-)^{p-1}$ in $ \Omega,$ $ u=0$ on $ \partial\Omega$ has a nontrivial solution $\,\,\, \} $ contains infinitely many curves which exist locally in the neighbourhood of suitable eigenvalues of the p-Laplacian operator.

Article information

Differential Integral Equations, Volume 14, Number 7 (2001), 867-882.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory
Secondary: 35J60: Nonlinear elliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations 47J10: Nonlinear spectral theory, nonlinear eigenvalue problems [See also 49R05]


Micheletti, Anna Maria; Pistoia, Angela. On the Fučí k spectrum for the $p$-Laplacian. Differential Integral Equations 14 (2001), no. 7, 867--882. https://projecteuclid.org/euclid.die/1356123195

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