MULTIPLICITY OF SOLUTIONS FOR ELLIPTIC SYSTEMS VIA LOCAL MOUNTAIN PASS METHOD

作者：Alves Claudianor O^*; Figueiredo Giovany M; Furtado Marcelo F

来源：Communications on Pure and Applied Analysis, 2009, 8(6): 1745-1758.

DOI：10.3934/cpaa.2009.8.1745

• Elliptic systems
• Schrodinger equation
• Ljusternik-Schnirelmann theory
• positive solutions

We consider the system
-epsilon(2)Delta u W(x)u = Q(u)(u, v) in R(N),
-epsilon(2)Delta v V(x)v = Q(v)(u, v) in R(N),
u, v is an element of H(1)(R(N)), u(x), v(x) > 0 for each x is an element of R(N),
where epsilon > 0, W and V are positive potentials and Q is a homogeneous function with subcritical growth. We relate the number of solutions with the topology of the set where W and V attain their minimum values. In the proof we apply Ljusternik-Schnirelmann theory.

• 出版日期2009-11