The convergence analysis and uniqueness of blow-up solutions for a Dirichlet problem of the general \(k\)-Hessian equations

DOI10.1016/j.aml.2019.106124zbMath1440.35018OpenAlexW2989387953MaRDI QIDQ2187078

Jiafa Xu, Yujun Cui, Xin Guang Zhang, Yong-Hong Wu, Ji-Qiang Jiang

Publication date: 2 June 2020

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2019.106124

zbMATH Keywords

radial solutionserror estimateunique solution

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Higher-order hyperbolic equations (35L25) Blow-up in context of PDEs (35B44)

Related Items (40)

Existence and multiplicity of radial solutions for a \(k\)-Hessian system ⋮ Entire positive \(k\)-convex solutions to \(k\)-Hessian type equations and systems ⋮ Existence of positive solutions for third-order semipositone boundary value problems on time scales ⋮ The radial solution for an eigenvalue problem of singular augmented Hessian equation ⋮ Monotone iterative method for fractional differential equations with integral boundary conditions ⋮ Uniqueness of iterative positive solution to nonlinear fractional differential equations with negatively perturbed term ⋮ New sequential fractional differential equations with mixed-type boundary conditions ⋮ Multiplicity solutions for integral boundary value problem of fractional differential systems ⋮ A new family of Sakurai-Torii-Sugiura type iterative methods with high order of convergence ⋮ Multiplicity of quasilinear Schrödinger equation ⋮ Exact combined solutions for the \((2+1)\)-dimensional dispersive long water-wave equations ⋮ The existence of solution of diffusion equation with the general conformable derivative ⋮ Analytical solutions to the Caudrey-Dodd-Gibbon-Sawada-Kotera equation via symbol calculation approach ⋮ A relaxed self-adaptive projection algorithm for solving the multiple-sets split equality problem ⋮ The existence and multiplicity of \(k\)-convex solutions for a coupled \(k\)-Hessian system ⋮ A fixed-point theorem for ordered contraction-type decreasing operators in Banach space with lattice structure ⋮ Inelastic interaction and blowup new solutions of nonlinear and dispersive long gravity waves ⋮ The existence of radial \(k\)-admissible solutions for \(n\)-dimension system of \(k\)-Hessian equations ⋮ Existence of \(k\)-convex solutions for the \(k\)-Hessian equation ⋮ Existence and uniqueness of positive solutions for singular nonlinear fractional differential equation via mixed monotone operator method ⋮ Positive solutions for a weakly singular Hadamard-type fractional differential equation with changing-sign nonlinearity ⋮ A novel Speckle noise removal algorithm based on ADMM and energy minimization method ⋮ Three-order multipoint boundary value problems for \(p\)-Laplacian operator on time scales ⋮ The extreme solutions for a σ‐Hessian equation with a nonlinear operator ⋮ On highly dimensional elastic and nonelastic interaction between internal waves in straight and varying cross-section channels ⋮ A novel global energy and local energy-based Legendre polynomial approximation for image segmentation ⋮ Solutions for a singular Hadamard-type fractional differential equation by the spectral construct analysis ⋮ Iterative properties of solution for a general singular \(n\)-Hessian equation with decreasing nonlinearity ⋮ Existence of solutions for fractional evolution equations with infinite delay and almost sectorial operator ⋮ Existence of solutions for a periodic boundary value problem with impulse and fractional derivative dependence ⋮ An SDP method for copositivity of partially symmetric tensors ⋮ A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator ⋮ A conservative Crank-Nicolson Fourier spectral method for the space fractional Schrödinger equation with wave operators ⋮ The eigenvalue problem of a singular \(k\)-Hessian equation ⋮ Existence and nonexistence of positive solutions for high-order fractional differential equation boundary value problems at resonance ⋮ Classification and existence of positive entire \(k\)-convex radial solutions for generalized nonlinear \(k\)-Hessian system ⋮ Solvability and asymptotic properties for an elliptic geophysical fluid flows model in a planar exterior domain ⋮ On the exact solutions of two \((3+1)\)-dimensional nonlinear differential equations ⋮ Multiple solutions for a modified quasilinear Schrödinger elliptic equation with a nonsquare diffusion term ⋮ On a power-type coupled system of k-Hessian equations

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