scholarly journals Multiple solutions for a fourth order equation with nonlinear boundary conditions: theoretical and numerical aspects

2019 ◽  
pp. 335-348
Author(s):  
Cristiane Aparecida Pendeza Martinez ◽  
André Luís Machado Martinez ◽  
Glaucia Maria Bressan ◽  
Emerson Vitor Castelani ◽  
Roberto Molina de Souza
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Order Equation ◽  
Fourth Order Equation

scholarly journals Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Dongliang Yan
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Order Equation ◽  
Positive Parameter ◽  
Fourth Order Equation ◽  
Existence Of Positive Solutions ◽  
Small Positive Parameter

We show the existence of positive solutions for a singular superlinear fourth-order equation with nonlinear boundary conditions. u⁗x=λhxfux, x∈0,1,u0=u′0=0,u″1=0, u⁗1+cu1u1=0, where λ > 0 is a small positive parameter, f:0,∞⟶ℝ is continuous, superlinear at ∞, and is allowed to be singular at 0, and h: [0, 1] ⟶ [0, ∞) is continuous. Our approach is based on the fixed-point result of Krasnoselskii type in a Banach space.

scholarly journals Iterative Method for Solving a Beam Equation with Nonlinear Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Quang A. Dang ◽  
Nguyen Thanh Huong
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Order Equation ◽  
Beam Equation ◽  
Linear Boundary ◽  
Order Problem ◽  
Fourth Order Problem

In this paper, we propose an iterative method for solving a beam problem which is described by a nonlinear fourth-order equation with nonlinear boundary conditions. The method reduces this nonlinear fourth-order problem to a sequence of linear second-order problems with linear boundary conditions. The convergence of the method is proved, and some numerical examples demonstrate the efficiency of the method.

Multiple Solutions of Nonlinear Fractional Differential Equations with p-Laplacian Operator and Nonlinear Boundary Conditions

2015 ◽  
Vol 65 (1) ◽  
Author(s):  
Yiliang Liu ◽  
Liang Lu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Upper And Lower Solutions ◽  
Nonlinear Boundary Conditions ◽  
Laplacian Operator ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential

AbstractIn this paper, we deal with multiple solutions of fractional differential equations with p-Laplacian operator and nonlinear boundary conditions. By applying the Amann theorem and the method of upper and lower solutions, we obtain some new results on the multiple solutions. An example is given to illustrate our results.

scholarly journals Existence of Multiple Solutions for a -Kirchhoff Problem with Nonlinear Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zonghu Xiu ◽  
Caisheng Chen
Keyword(s):  
Variational Method ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Nehari Manifold ◽  
The Nehari Manifold ◽  
Kirchhoff Problem

The paper considers the existence of multiple solutions of the singular nonlocal elliptic problem , ,   = , on , where , . By the variational method on the Nehari manifold, we prove that the problem has at least two positive solutions when some conditions are satisfied.

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