scholarly journals One solution for nonlocal fourth order equations

2021 ◽  
Vol 40 ◽  
pp. 1-13
Author(s):  
Ghasem A. Afrouzi ◽  
David Barilla ◽  
Giuseppe Caristi ◽  
Shahin Moradi
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Critical Point ◽  
Fourth Order ◽  
Boundary Value ◽  
Kirchhoff Type ◽  
Fourth Order Equations ◽  
Critical Point Result

A critical point result for differentiable functionals is exploited in order to prove that a suitable class of fourth-order boundary value problem of Kirchhoff-type possesses at least one weak solution under an asymptotical behavior of the nonlinear datum at zero. Some examples to illustrate the results are given.

scholarly journals Existence of three solutions to the discrete fourth-order boundary value problem with four parameters

2018 ◽  
Vol 38 (2) ◽  
pp. 173-185 ◽  
Author(s):  
Mohamed Ousbika ◽  
Zakaria El Allali
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Critical Point ◽  
Fourth Order ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Three Solutions

In this work, we willproving the existence of three solutionsf or the discrete nonlinear fourth order boundary value problems with four parameters. The methods used here are based on the critical point theory.

scholarly journals Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Liming Xiao ◽  
Mingkun Li
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Evolution Problem ◽  
Positive Energy ◽  
Initial Boundary Value

AbstractIn this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics. By the mountain pass theorem we first prove the existence of nonzero weak solution to the static problem, which is the important basis of evolution problem, then based on the method of potential well we prove the existence of global weak solution to the evolution problem.

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