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Existence and uniqueness of solutions of nonlinear elliptic equations without growth conditions at infinity |
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| Authors: | Salomón Alarcón Jorge García-Melián Alexander Quaas |
| Institution: | 1. Departamento de Matem??tica, Universidad T??cnica Federico Santa Mar??a, Casilla V-110, Avda. Espa?a, 1680, Valpara??so, Chile 2. Departamento De An??lisismatem??tico, Universidad De Lalaguna, C/. Astrof??sico Francisco S??nchez S/N, 38271, La Laguna, Spain 3. Instituto Universitario De Estudios Avanzados (Iudea) En F??sica At??mica Molecular Y Fot??nica Facultad De F??sica Universidad De La Laguna, C/. Astrof??sico Francisco S??nchez S/N, 38203, La Laguna, Spain |
| Abstract: | In this paper, we consider the nonlinear elliptic problem $$ - \Delta u + {\left| u \right|^{p - 1}}u + {\left| {\nabla u} \right|^q} = f$$ in ? N , where p > 1 and q > 0. We show that if f ?? L loc r (? N ) for suitable r ?? 1, then there exists a distributional solution of the equation, independently of the behavior of f at infinity. We also analyze the uniqueness of this solution in some cases. |
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