Localized critical points in Banach spaces and sign changing solutions of nonlinear p-Laplacian equations

2003 ◽  
Author(s):  
Zhaoli Liu
Keyword(s):  
Banach Spaces ◽  
Critical Points ◽  
Sign Changing Solutions ◽  
Laplacian Equations

scholarly journals A Class of Fractionalp-Laplacian Integrodifferential Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yiliang Liu ◽  
Liang Lu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Existence Results ◽  
Integrodifferential Equations ◽  
Laplacian Operator ◽  
Laplacian Equations

We study a class of nonlinear fractional integrodifferential equations withp-Laplacian operator in Banach space. Some new existence results are obtained via fixed point theorems for nonlocal boundary value problems of fractionalp-Laplacian equations. An illustrative example is also discussed.

scholarly journals Existence of Solutions to the Boundary Value Problems for a Class of P-Laplacian Equations at Resonance

2016 ◽  
Vol 8 (3) ◽  
pp. 37
Author(s):  
Lina Zhou ◽  
Weihua Jiang
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
At Resonance ◽  
Laplacian Equations

By the generalizing the extension of the continuous theorem of Ge and Ren and constructing suitable Banach spaces and operators, we investigate the existence-solutions to the boundary value problems for a class of  p-Laplacian equations. Finally an example is given to illustrate our results.

On the system of p-Laplacian equations with critical growth

2018 ◽  
Vol 29 (02) ◽  
pp. 1850008 ◽  
Author(s):  
Xiangqing Liu ◽  
Junfang Zhao ◽  
Jiaquan Liu
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary ◽  
Critical Growth ◽  
Laplacian Operator ◽  
First Eigenvalue ◽  
Bounded Smooth Domain ◽  
The First Eigenvalue ◽  
Bounded Smooth ◽  
Sign Changing Solutions ◽  
Laplacian Equations

In this paper, we consider the system of [Formula: see text]-Laplacian equations with critical growth [Formula: see text] where [Formula: see text] is a bounded smooth domain in [Formula: see text] the first eigenvalue of the [Formula: see text]-Laplacian operator [Formula: see text] with the Dirichlet boundary condition, [Formula: see text] for [Formula: see text]. The existence of infinitely many sign-changing solutions is proved by the truncation method and by the concentration analysis on the approximating solutions, provided [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document