scholarly journals Multiplicity of Solutions to a Potential Operator Equation and Its Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Jincheng Huang
Keyword(s):  
Operator Equation ◽  
Elliptic Systems ◽  
Nehari Manifold ◽  
Laplacian Operator ◽  
Potential Operator ◽  
Multiplicity Of Solutions ◽  
Homogeneous Potential ◽  
Quasilinear Elliptic Systems ◽  
Nonnegative Solutions ◽  
Quasilinear Elliptic

We consider the multiplicity of solutions for operator equation involving homogeneous potential operators. With the help of Nehari manifold and fibering maps, we prove that such equation has at least two nontrivial solutions. Furthermore, we apply this result to prove the existence of two nonnegative solutions for three types of quasilinear elliptic systems involving (p, q)-Laplacian operator and concave-convex nonlinearities.

scholarly journals Multiple Solutions for a Class of Dirichlet Double Eigenvalue Quasilinear Elliptic Systems Involving the ()-Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Armin Hadjian ◽  
Saleh Shakeri
Keyword(s):  
Multiple Solutions ◽  
Main Tool ◽  
Elliptic Systems ◽  
Existence Results ◽  
Laplacian Operator ◽  
Quasilinear Elliptic System ◽  
Critical Point Theorem ◽  
Quasilinear Elliptic Systems ◽  
Double Eigenvalue ◽  
Quasilinear Elliptic

Existence results of three weak solutions for a Dirichlet double eigenvalue quasilinear elliptic system involving the ()-Laplacian operator, under suitable assumptions, are established. Our main tool is based on a recent three-critical-point theorem obtained by Ricceri. We also give some examples to illustrate the obtained results.

scholarly journals Multiple solutions for a class of nonlocal quasilinear elliptic systems in Orlicz–Sobolev spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. Heidari ◽  
A. Razani
Keyword(s):  
Variational Methods ◽  
Sobolev Spaces ◽  
Multiple Solutions ◽  
Elliptic Systems ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

AbstractIn this paper, we study some results on the existence and multiplicity of solutions for a class of nonlocal quasilinear elliptic systems. In fact, we prove the existence of precise intervals of positive parameters such that the problem admits multiple solutions. Our approach is based on variational methods.

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