Existence of Solutions for a Sublinear System of Elliptic Equations
Yarur, Cecilia S.
Southwest Texas State University, Department of Mathematics
We study the existence of non-trivial non-negative solutions for the system -Δu = |x|α vp Δv = |x|b uq, where p and q are positive constants with pq < 1, and the domain is the unit ball of ℝN (N > 2) except for the center zero. We look for pairs of functions that satisfy the above system and Dirichlet boundary conditions set to zero. Our results also apply to some super-linear systems.
Semilinear elliptic systems, Sub-harmonic functions, Super-harmonic functions
Cid, C., & Yarur, C. (2000). Existence of solutions for a sublinear system of elliptic equations. <i>Electronic Journal of Differential Equations, 2000</i>(33), pp. 1-11.