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A study on solvability of the fourth-order nonlinear boundary value problems

  • Haide Gou EMAIL logo
Published/Copyright: October 14, 2022
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 24 Issue 8

Abstract

The purpose of the paper is devoted to proving the solvability of the fourth order boundary value problem. Firstly, we build a maximum principle for the corresponding linear equation, by the use of this maximum principle, we develop a monotone iterative technique in the presence of lower and upper solutions to solve the nonlinear equation, secondly, the existence and uniqueness results for the problem is obtained. In addition, an example is presented to show the application of our main results.

Keywords: fourth order equation; lower and upper solution; maximum principle; monotone iterative technique
AMS (2000) Subject Classification: 34B15
Corresponding author: Haide Gou, College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, P. R. China, E-mail:

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11661071，12061062

Funding source: Science Research Project for Colleges and Universities of Gansu Province

Award Identifier / Grant number: No. 2022A-010

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: Supported by the National Natural Science Foundation of China (Grant No. 11661071, 12061062). Science Research Project for Colleges and Universities of Gansu Province (No. 2022A-010).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2020-10-17
Accepted: 2022-09-29
Published Online: 2022-10-14

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2021-0052
Keywords for this article
fourth order equation; lower and upper solution; maximum principle; monotone iterative technique

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Testing of logarithmic-law for the slip with friction boundary condition
  4. A new clique polynomial approach for fractional partial differential equations
  5. The modified Rusanov scheme for solving the phonon-Bose model
  6. Delta-shock for a class of strictly hyperbolic systems of conservation laws
  7. The Cădariu–Radu method for existence, uniqueness and Gauss Hypergeometric stability of a class of Ξ-Hilfer fractional differential equations
  8. Novel periodic and optical soliton solutions for Davey–Stewartson system by generalized Jacobi elliptic expansion method
  9. The simulation of two-dimensional plane problems using ordinary state-based peridynamics
  10. Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format
  11. Simulation of the crystallization processes by population balance model using a linear separation method
  12. PS and GW optimization of variable sliding gains mode control to stabilize a wind energy conversion system under the real wind in Adrar, Algeria
  13. Characteristics of internal flow of nozzle integrated with aircraft under transonic flow
  14. Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field
  15. The influence pulse-like near-field earthquakes on repairability index of reversible in mid-and short-rise buildings
  16. Intelligent controller for maximum power extraction of wind generation systems using ANN
  17. A new self-adaptive inertial CQ-algorithm for solving convex feasibility and monotone inclusion problems
  18. Existence and Hyers–Ulam stability of solutions for nonlinear three fractional sequential differential equations with nonlocal boundary conditions
  19. A study on solvability of the fourth-order nonlinear boundary value problems
  20. Adaptive control for position and force tracking of uncertain teleoperation with actuators saturation and asymmetric varying time delays
  21. Framing the hydrothermal significance of water-based hybrid nanofluid flow over a revolving disk
  22. Catalytic surface reaction on a vertical wavy surface placed in a non-Darcy porous medium
  23. Carleman framework filtering of nonlinear noisy phase-locked loop system
  24. Corrigendum
  25. Corrigendum to: numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
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