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| We present an approach for the determining of the precise range of the existence stable and blow-up solutions for families of elliptic and heat equations with p-Laplacian and supercritical nonlinearities. The approach is based on the extended functional method where precise boundaries of the range of the existence stable and blow-up solutions are defined by direct and dual minimax type formulas. A number of examples, including system of elliptic and parabolic problems with $p$- Laplacian, will be discussed.
In addition, we present a numerical algorithm for the computation of solutions of the minimax variational problems corresponding to the extended functional method. |
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