Acta mathematica scientia, Series B >
EXISTENCE OF POSITIVE SOLUTIONS TO SEMILINEAR ELLIPTIC SYSTEMS IN RN WITH ZERO MASS
Received date: 2012-07-05
Revised date: 2012-09-27
Online published: 2013-07-20
Supported by
Partially supported by NSFC (11071095) and Hubei Key Laboratory of Mathematical Sciences.
In this paper, we prove the existence of at least one positive solution pair (u, v) ∈ D1,2(RN) × D1,2(RN) to the following semilinear elliptic system
{−△u = K(x)f(v), x ∈ RN,
−△v = K(x)g(u), x ∈ RN (0.1)
by using a linking theorem, where K(x) is a positive function in Ls(RN) for some s > 1 and the nonnegative functions f, g ∈ C(R, R) are of quasicritical growth, superlinear at infinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual.
Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problem
−△u = K(x)f(u), x ∈ RN,
and a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in RN.
LI Gong-Bao , YE Hong-Yu . EXISTENCE OF POSITIVE SOLUTIONS TO SEMILINEAR ELLIPTIC SYSTEMS IN RN WITH ZERO MASS[J]. Acta mathematica scientia, Series B, 2013 , 33(4) : 913 -928 . DOI: 10.1016/S0252-9602(13)60050-8
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