Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
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Zhiqian He
and
Liangying Miao
Abstract
This paper investigates the existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for the k-Hessian equation subject to a homogeneous Dirichlet boundary condition:
where B = {x ∈ ℝn: ∣x∣ < 1}, λ is a positive parameter, k ∈ {1, …, n}, f: [0, ∞) → [0, ∞) is continuous. In contrast to previous studies, our main results are established under the essential condition that the radially symmetric k-admissible solutions of (P) are generically non-convex. The main tool is the fixed point theorem in cones.
Funding statement: This work was supported by the National Natural Science Foundation of China (Nos.12461035, 12301631), Applied Basic Research Project of Qinghai Province (2025-ZJ-722).
Acknowledgement
The authors are very grateful to the anonymous referees for their valuable suggestions.
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(Communicated by Michal Fečkan)
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Articles in the same Issue
- Copies of monomorphic structures
- Endomorphism kernel property for extraspecial and special groups
- Sums of Tribonacci numbers close to powers of 2
- Multiplicative functions k-additive on hexagonal numbers
- Monogenic even cyclic sextic polynomials
- Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
- Degree of independence in non-archimedean fields
- Remarks on some one-ended groups
- Some new characterizations of weights for hardy-type inequalities with kernels on time scales
- Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
- Radius estimates for functions in the class 𝒰r(λ)
- Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
- More q-congruences from Singh’s quadratic transformation
- Stability and controllability of cycled dynamical systems
- Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
- Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
- Coincidence points via tri-simulation functions with an application in integral equations
- On Fong-Tsui conjecture and binormality of operators
- Riemannian maps of CR-submanifolds of Kaehler manifolds
- On structural numbers of topological spaces
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