This paper considers a class of Schrödinger elliptic system involving a nonlinear operator. Firstly, under the simple condition on and ', we prove the existence of the entire positive bounded radial solutions. Secondly, by using the iterative technique and the method of contradiction, we prove the existence and nonexistence of the entire positive blow-up radial solutions. Our results extend the previous existence and nonexistence results for both the single equation and systems. In the end, we give two examples to illustrate our results.
In this paper, we study the positive solutions of the Schrödinger elliptic system div(G(|∇y| p−2)∇y) = b 1 (|x|)ψ(y) + h 1 (|x|)ϕ(z), x ∈ R n (n ≥ 3), div(G(|∇z| p−2)∇z) = b 2 (|x|)ψ(z) + h 2 (|x|)ϕ(y), x ∈ R n , where G is a nonlinear operator. By using the monotone iterative technique and Arzela-Ascoli theorem, we prove that the system has the positive entire bounded radial solutions. Then, we establish the results for the existence and nonexistence of the positive entire blow-up radial solutions for the nonlinear Schrödinger elliptic system involving a nonlinear operator. Finally, three examples are given to illustrate our results.
In this paper, we investigate a class of nonlinear Schrödinger systems containing a nonlinear operator under Osgood-type conditions. By employing the iterative technique, the existence conditions for entire positive radial solutions of the above problem are given under the cases where components μ and ν are bounded, μ and ν are blow-up, and one of the components is bounded, while the other is blow-up. Finally, we present two examples to verify our results.
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