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Estudiamos la existencia de soluciones del sistema elíptico no lineal Δu + |∇u| = p(|x|)f(v), Δv + |∇v| = q(|x|)g(u) en Ω que explotan en el borde. Aquí Ω es un dominio acotado de RN o el espacio total. Las nolinealidades f y g son funciones continuas positivas mientras que los potenciales p y q son funciones continuas que satisfacen apropiadas condiciones de crecimiento en el infinito. Demostramos que las soluciones explosivas en el borde dejan de existir si f y g son sublineales. Esto se tiene...
Sharp bounds on some distance-based graph invariants of -vertex -trees are established in a unified approach, which may be viewed as the weighted Wiener index or weighted Harary index. The main techniques used in this paper are graph transformations and mathematical induction. Our results demonstrate that among -trees with vertices the extremal graphs with the maximal and the second maximal reciprocal sum-degree distance are coincident with graphs having the maximal and the second maximal reciprocal...
In this paper we consider periodic and Dirichlet problems for second order vector differential inclusions. First we show the existence of extremal solutions of the periodic problem (i.e. solutions moving through the extreme points of the multifunction). Then for the Dirichlet problem we show that the extremal solutions are dense in the -norm in the set of solutions of the “convex” problem (relaxation theorem).
In this paper we study semilinear second order differential inclusions involving a multivalued maximal monotone operator. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain “extremal” solutions and we prove a strong relaxation theorem.
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