EXISTENCE OF POSITIVE SOLUTIONS TO SEMILINEAR ELLIPTIC SYSTEMS IN RN WITH ZERO MASS

doi:10.1016/S0252-9602(13)60050-8

Abstract

Abstract:

In this paper, we prove the existence of at least one positive solution pair (u, v) ∈ D^1,2(R^N) × D^1,2(R^N) to the following semilinear elliptic system
{−△u = K(x)f(v), x ∈ R^N,
−△v = K(x)g(u), x ∈ R^N(0.1)
by using a linking theorem, where K(x) is a positive function in Ls(R^N) 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 ∈ R^N,

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 R^N.

Key words: existence, positive solutions, elliptic system, linking geometric structure, zero mass case

CLC Number:

35J60

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.

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