Stationary Sign Changing Solutions for an Inhomogeneous Nonlocal Problem
link https://doi.org/10.1512/iumj.2011.60.4385get_appStationary Sign Changing Solutions for an Inhomogeneous Nonlocal Problem.pdf
account_box Cortazar, Carmenaccount_box Elgueta, Manuelaccount_box Garcia Melian, Jorgeaccount_box Martinez, Salome
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We consider the following nonlocal equation:
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| Autor | Cortazar, Carmen Elgueta, Manuel Garcia Melian, Jorge Martinez, Salome |
| Título | Stationary Sign Changing Solutions for an Inhomogeneous Nonlocal Problem |
| Revista | INDIANA UNIVERSITY MATHEMATICS JOURNAL |
| ISSN | 0022-2518 |
| ISSN electrónico | 1943-5258 |
| Volumen | 60 |
| Número de publicación | 1 |
| Página inicio | 209 |
| Página final | 232 |
| Fecha de publicación | 2011 |
| Resumen | We consider the following nonlocal equation: integral(R)J (x - y/g(y)) u(y)/g(y) dy - u(x) = 0 x epsilon R, where J is an even, compactly supported, Holder continuous probability kernel, g is a continuous function, bounded and bounded away from zero in R. We prove the existence of a sign changing solution q(x) which is strictly positive when x > K and strictly negative for x < -K, provided that K is chosen large enough. The solution q(x) so constructed verifies a(1) <= q(x)/x <= a(2) for positive constants a(1), a(2) and large vertical bar x vertical bar. In addition, we show that all solutions with polynomial growth are of the form Aq(x) + Bp (x), where p is the unique normalized positive (bounded) solution of the equation. In the particular case where g = 1 we also construct solutions with exponential growth. |
| Derechos | registro bibliográfico |
| Agencia financiadora | Ministerio de Ciencia e Innovacion FEDER (Spain) FONDECYT Basal project CMM U. de Chile CAPDE Anillo (Chile) |
| DOI | 10.1512/iumj.2011.60.4385 |
| Editorial | INDIANA UNIV MATH JOURNAL |
| Enlace | |
| Id de publicación en WoS | WOS:000303134000010 |
| Paginación | 24 páginas |
| Palabra clave | nonlocal diffusion sign changing solution uniqueness ASYMPTOTIC-BEHAVIOR DIRICHLET PROBLEM TRAVELING-WAVES EQUATION UNIQUENESS EXISTENCE MODEL DISPERSAL |
| Tema ODS | 03 Good Health and Well-being |
| Tema ODS español | 03 Salud y bienestar |
| Tipo de documento | artículo |