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On the asymptotic behavior of certain solutions of the Dirichlet problem for the equation \({-\Delta_pu=\lambda| u|^{q-2}u}\). (English) Zbl 1281.35013
Summary: Let \(p>1\). We study the behavior of certain positive and nodal solutions of the problem \[ \begin{cases} -\Delta_p u = \lambda |u|^{q-2} & \text{in } \varOmega, \\ u = 0 & \text{on } \partial\varOmega,\end{cases} \] on varying of the parameters \(\lambda>0\) and \(q>1\).

MSC:
35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
35B09 Positive solutions to PDEs
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