scholarly journals A sum operator equation and applications to nonlinear elastic beam equations and Lane–Emden–Fowler equations

2011 ◽  
Vol 375 (2) ◽  
pp. 388-400 ◽  
Author(s):  
Chengbo Zhai ◽  
Douglas R. Anderson
Keyword(s):  
Operator Equation ◽  
Elastic Beam ◽  
Beam Equations ◽  
Nonlinear Elastic ◽  
Elastic Beam Equations

scholarly journals Common Fixed Points of (α,η) − (θ,ϝ) Rational Contractions with Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Mujahid Abbas ◽  
Hira Iqbal ◽  
Manuel De La Sen
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Periodic Problem ◽  
Elastic Beam ◽  
Common Fixed Points ◽  
First Order ◽  
Beam Equations ◽  
Nonlinear Elastic ◽  
Rational Contraction ◽  
Elastic Beam Equations

We present the notion of set valued (α,η)-(θ,ϝ) rational contraction mappings and then some common fixed point results of such mappings in the setting of metric spaces are established. Some examples are presented to support the concepts introduced and the results proved in this paper. These results unify, extend, and refine various results in the literature. Some fixed point results for both single and multivalued (θ,ϝ) rational contractions are also obtained in the framework of a space endowed with partial order. As application, we establish the existence of solutions of nonlinear elastic beam equations and first-order periodic problem.

scholarly journals Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jian Liu ◽  
Wenguang Yu
Keyword(s):  
Iterative Method ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Elastic Beam ◽  
Kirchhoff Type ◽  
Newton Iterative Method ◽  
Beam Equations ◽  
Critical Point Theorems ◽  
Elastic Beam Equations

AbstractIn this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorems. Combining with the Newton-iterative method, an example is presented to illustrate the value of the obtained theorems.

Variational approaches to impulsive elastic beam equations of Kirchhoff type

2016 ◽  
Vol 61 (7) ◽  
pp. 931-968 ◽  
Author(s):  
Shapour Heidarkhani ◽  
Ghasem A. Afrouzi ◽  
Massimiliano Ferrara ◽  
Shahin Moradi
Keyword(s):  
Elastic Beam ◽  
Kirchhoff Type ◽  
Beam Equations ◽  
Variational Approaches ◽  
Elastic Beam Equations

scholarly journals Non-trivial solutions for nonlinear fourth-order elastic beam equations

2011 ◽  
Vol 62 (4) ◽  
pp. 1862-1869 ◽  
Author(s):  
Gabriele Bonanno ◽  
Beatrice Di Bella ◽  
Donal O’Regan
Keyword(s):  
Fourth Order ◽  
Elastic Beam ◽  
Beam Equations ◽  
Elastic Beam Equations
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