A generalized Fucik type eigenvalue problem for p-Laplacian

Yuanji Cheng, Malmö University, Malmö, Sweden

E. J. Qualitative Theory of Diff. Equ., No. 18. (2009), pp. 1-9.

Abstract: In this paper we study the generalized Fucik type eigenvalue for the boundary value problem of one dimensional $p-$Laplace type differential equations
\begin{displaymath}\left\{
\begin{array}{lll} - (\varphi( u')) ' = \psi(u), \quad -T< x < T; \\
\quad u(-T)=0, \quad u(T)=0 \\
\end{array} \right.\eqno(*)
\end{displaymath}
where $\varphi (s) = \alpha s_+^{p-1} -\beta s_-^{p-1}, \psi (s) = \lambda s_+^{p-1} -\mu s_-^{p-1}, p >1.$ We obtain a explicit characterization of Fucik spectrum $(\alpha, \beta, \lambda, \mu),$ i.e., for which the (*) has a nontrivial solution.

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