Bound states for a coupled Schrödinger system
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چکیده
We consider the existence of bound states for the coupled elliptic system ∆u1 − λ1u1 + μ1u 3 1 + βu 2 2u1 = 0 in R n , ∆u2 − λ2u2 + μ2u 3 2 + βu 2 1u2 = 0 in R n , u1 > 0, u2 > 0, u1, u2 ∈ H (R). where n ≤ 3. Using the fixed point index in cones we prove the existence of a five-dimensional continuum C ⊂ R5+ × H (R) × H(R) of solutions (λ1, λ2, μ1, μ2, β, u1, u2) bifurcating from the set of semipositive solutions (where u1 = 0 or u2 = 0) and investigate the parameter range covered by C. Mathematics Subject Classification (2000). Primary 35Q55; Secondary 35B32, 35J50, 35J55, 47J30, 58E05, 58E07.
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تاریخ انتشار 2007