artículo
Stationary Sign Changing Solutions for an Inhomogeneous Nonlocal Problem
Fecha
2011Registro en:
10.1512/iumj.2011.60.4385
1943-5258
0022-2518
WOS:000303134000010
Autor
Cortazar, Carmen
Elgueta, Manuel
Garcia Melian, Jorge
Martinez, Salome
Institución
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.