Existence and uniqueness of solutions to the nonlinear boundary value problem for fourth-order differential equations with all derivatives

DOI10.1186/s13660-022-02907-9OpenAlexW4319594920WikidataQ117219154 ScholiaQ117219154MaRDI QIDQ6062407

Yujun Cui, Hui ling Chen

Publication date: 30 November 2023

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-022-02907-9

zbMATH Keywords

existence and uniquenessPerov's fixed point theoremfully fourth-order differential equation

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear boundary value problems for ordinary differential equations (34B15) Applications of operator theory to differential and integral equations (47N20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence and uniqueness of positive solutions for fourth-order \(m\)-point boundary value problems with two parameters
• Existence of multiple positive solutions for fourth-order boundary value problems in Banach spaces
• Existence results and iterative method for solving the cantilever beam equation with fully nonlinear term
• A monotone iterative technique for solving the bending elastic beam equations
• Nontrivial solutions of singular fourth-order Sturm-Liouville boundary value problems with a sign-changing nonlinear term
• Iterative solutions for a beam equation with nonlinear boundary conditions of third order
• Positive solutions for \(p\)-Laplacian fourth-order differential system with integral boundary conditions
• Existence of positive solutions for the cantilever beam equations with fully nonlinear terms
• Positive solutions of some nonlocal fourth-order boundary value problem
• Positive solutions for systems of a nonlinear fourth-order singular semipositone boundary value problems
• The existence of countably many positive solutions for singular multipoint boundary value problems
• Existence results and numerical solutions for a beam equation with nonlinear boundary conditions.
• The dual variational principle and equilibria for a beam resting on a discontinuous nonlinear elastic foundation
• On the existence of positive solutions for a fourth-order boundary value problem
• Existence and iterative method for some fourth order nonlinear boundary value problems
• Nontrivial solutions of fourth-order singular boundary value problems with sign-changing nonlinear terms
• Positive solutions for fourth-order singular \(p\)-Laplacian differential equations with integral boundary conditions
• Sharper existence and uniqueness results for solutions to fourth-order boundary value problems and elastic beam analysis
• The method of lower and upper solutions for the cantilever beam equations with fully nonlinear terms
• Positive solutions of fourth-order problems with dependence on all derivatives in nonlinearity under Stieltjes integral boundary conditions
• Symmetric positive solutions for fourth-order \(n\)-dimensional \(m\)-Laplace systems
• Positive solutions for a fourth-order Riemann-Stieltjes integral boundary value problem
• Monotonically iterative method of nonlinear cantilever beam equations
• The role of matrices that are convergent to zero in the study of semilinear operator systems
• Multiplicity of solutions of a two point boundary value problem for a fourth-order equation
• Multiplicity results for a class of fourth order semipositonem-point boundary value problems
• Continuation Theory for Contractions on Spaces with Two Vector-Valued Metrics
• Uniqueness result for the cantilever beam equation with fully nonlinear term
• On the equivalence between Perov fixed point theorem and Banach contraction principle