Multiple solutions of a quasilinear elliptic system involving the nonlinear boundary conditions on exterior domain

2012 ◽  
Vol 36 (1) ◽  
pp. 5-17
Author(s):  
Shuai Liu ◽  
Caisheng Chen
Keyword(s):  
Boundary Conditions ◽  
Elliptic System ◽  
Multiple Solutions ◽  
Exterior Domain ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Quasilinear Elliptic System ◽  
Quasilinear Elliptic

scholarly journals Existence and Multiplicity of Nonnegative Solutions for Quasilinear Elliptic Exterior Problems with Nonlinear Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Jincheng Huang
Keyword(s):  
Boundary Conditions ◽  
Exterior Domain ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Multiplicity Results ◽  
Exterior Problems ◽  
Existence And Multiplicity ◽  
Nonnegative Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

Existence and multiplicity results are established for quasilinear elliptic problems with nonlinear boundary conditions in an exterior domain. The proofs combine variational methods with a fibering map, due to the competition between the different growths of the nonlinearity and nonlinear boundary term.

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.

On the Existence of Boundary Blow-up Solutions for a General Class of Quasilinear Elliptic Systems

2014 ◽  
Vol 14 (4) ◽  
Author(s):  
Sonia Ben Othman ◽  
Rym Chemmam ◽  
Paul Sauvy
Keyword(s):  
Boundary Conditions ◽  
Elliptic System ◽  
General Class ◽  
Blow Up ◽  
Elliptic Systems ◽  
Quasilinear Elliptic System ◽  
Smooth Bounded Domain ◽  
Quasilinear Elliptic Systems ◽  
System P ◽  
Quasilinear Elliptic

AbstractIn this paper, we investigate the following quasilinear elliptic system (P) with explosive boundary conditions:ΔΔwhere Ω is a smooth bounded domain of ℝ

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