Nonnegative solutions for nonlinear elliptic systems

Abstract

In this paper, we show that the semilinear elliptic systems of the form1) possess at least one nonnegative nontrivial solution pair (u, v) ∈ H 1 0 (Ω) × H 1 0 (Ω), where Ω is a smooth bounded domain in R N .

Positive Solutions for Asymptotically Linear Elliptic Systems

“…In [10], the authors considered problem (1.1) with superlinear nonlinearities. In this paper, we consider the case in which f (x, t) and g(x, t) are asymptotically linear at infinity for t.…”

Asymptotically linear elliptic systems in RN

“…Actually, Q (z) is indefinite in E if 0 λμ < 1 and the functional I(z) possesses geometry of Linking type, if λμ > 1, Q (z) is positively definite and I(z) possesses Mountain Pass geometry. In [14], C. Peng and J. Yang had considered problem (1.1) in bounded domain with 0 < λμ < 1, by using…”

Asymptotically Linear Elliptic Systems With Parameters

“…First, by the Pohozaev-type identity, the parameters λ and μ affect the sub-critical range of the growth of non-linear terms at infinity. Second, if λμ < 1, the decomposition of the space in the framework involves the parameters, see [5,6]. Moreover, f and g are superlinear in [5] and are asymptotically linear in [6].…”