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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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