Abstract
In this paper, a Hessian type system is studied. After converting the existence of an entire solution to the existence of a fixed point of a continuous mapping, the existence of entire k-convex radial solutions is established by the monotone iterative method. Moreover, a nonexistence result is also obtained.
Highlights
1 Introduction In this paper, we study the existence of entire k-convex radial solutions to the following problem of Hessian type system:
For general k-Hessian equation (1.2), when p ≡ 1 and f (u) = uγ k, γ > 1, Jin, Li, and Xu [13] showed the nonexistence of entire k-convex positive solutions
If we generalize p(|x|)f (u) to f (x, u), de Oliveira, do Ó, and Ubilla obtained the existence of k-convex radial solutions in the case of supercritical nonlinearity by means of variational techniques
Summary
1 Introduction In this paper, we study the existence of entire k-convex radial solutions to the following problem of Hessian type system: For general k-Hessian equation (1.2), when p ≡ 1 and f (u) = uγ k, γ > 1, Jin, Li, and Xu [13] showed the nonexistence of entire k-convex positive solutions. If we generalize p(|x|)f (u) to f (x, u), de Oliveira, do Ó, and Ubilla obtained the existence of k-convex radial solutions in the case of supercritical nonlinearity by means of variational techniques (see [5] and the references therein for research in this direction).
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