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.

Existence of Multiple Solutions for a p-Laplacian System in ℝN with Sign-changing Weight Functions

2016 ◽  
Vol 59 (2) ◽  
pp. 417-434 ◽  
Author(s):  
Hongxue Song ◽  
Caisheng Chen ◽  
Qinglun Yan
Keyword(s):  
Positive Solutions ◽  
Elliptic Problem ◽  
Multiple Solutions ◽  
Continuous Functions ◽  
Nehari Manifold ◽  
Weight Functions ◽  
Image Position ◽  
The Nehari Manifold ◽  
Linear Elliptic Problem

AbstractIn this paper, we consider the quasi-linear elliptic problemwhere and the weight H(x); h1(x); h2(x) are continuous functions that change sign in ℝN. We will prove that the problem has at least two positive solutions by using the Nehari manifold and the fibering maps associated with the Euler functional for this problem.

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.

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