Existence and multiplicity of nontrivial solutions for biharmonic equations with singular weight functions

2020 ◽  
Vol 105 ◽  
pp. 106335
Author(s):  
Han-Su Zhang ◽  
Tiexiang Li ◽  
Tsung-fang Wu
Keyword(s):  
Weight Functions ◽  
Nontrivial Solutions ◽  
Biharmonic Equations ◽  
Singular Weight ◽  
Existence And Multiplicity

scholarly journals Existence and multiplicity of nontrivial solutions of biharmonic equations via differential inclusion

2020 ◽  
Vol 19 (1) ◽  
pp. 391-405
Author(s):  
Ziqing Yuana ◽  
◽  
Jianshe Yu ◽  
Keyword(s):  
Differential Inclusion ◽  
Nontrivial Solutions ◽  
Biharmonic Equations ◽  
Existence And Multiplicity

scholarly journals Existence and multiplicity of nontrivial solutions for some biharmonic equations with p-Laplacian

2017 ◽  
Vol 262 (2) ◽  
pp. 945-977 ◽  
Author(s):  
Juntao Sun ◽  
Jifeng Chu ◽  
Tsung-fang Wu
Keyword(s):  
Nontrivial Solutions ◽  
Biharmonic Equations ◽  
Existence And Multiplicity

scholarly journals Existence of Nontrivial Solutions of p-Laplacian Equation with Sign-Changing Weight Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Ghanmi Abdeljabbar
Keyword(s):  
Boundary Conditions ◽  
Smooth Function ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Weight Functions ◽  
Nontrivial Solutions ◽  
Laplacian Equation ◽  
Existence And Multiplicity ◽  
Open Set

This paper shows the existence and multiplicity of nontrivial solutions of the p-Laplacian problem -Δpu=1/σ(∂F(x,u)/∂u)+λa(x)|u|q-2u for x∈Ω with zero Dirichlet boundary conditions, where Ω is a bounded open set in ℝn, 1<q<p<σ<p*(p*=np/(n-p) if p<n, p*=∞ if p≥n), λ∈ℝ∖{0}, a is a smooth function which may change sign in Ω̅,, and F∈C1(Ω̅ × ℝ,ℝ). The method is based on Nehari results on three submanifolds of the space W01,p(Ω).

scholarly journals Existence and multiplicity of solutions for a fractional p-Laplacian equation with perturbation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhen Zhi ◽  
Lijun Yan ◽  
Zuodong Yang
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Analytical Techniques ◽  
Nontrivial Solutions ◽  
Multiplicity Results ◽  
Multiplicity Of Solutions ◽  
Laplacian Equation ◽  
Existence And Multiplicity

AbstractIn this paper, we consider the existence of nontrivial solutions for a fractional p-Laplacian equation in a bounded domain. Under different assumptions of nonlinearities, we give existence and multiplicity results respectively. Our approach is based on variational methods and some analytical techniques.

scholarly journals Existence and multiplicity of solutions for Kirchhof-type problems with Sobolev–Hardy critical exponent

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hongsen Fan ◽  
Zhiying Deng
Keyword(s):  
Variational Method ◽  
Boundary Value Problem ◽  
Critical Exponent ◽  
Positive Solution ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problem ◽  
Nontrivial Solutions ◽  
Elliptic Boundary Value ◽  
Existence And Multiplicity

AbstractIn this paper, we discuss a class of Kirchhof-type elliptic boundary value problem with Sobolev–Hardy critical exponent and apply the variational method to obtain one positive solution and two nontrivial solutions to the problem under certain conditions.

Schrödinger systems with quadratic interactions

2019 ◽  
Vol 21 (08) ◽  
pp. 1850077
Author(s):  
Rushun Tian ◽  
Zhi-Qiang Wang ◽  
Leiga Zhao
Keyword(s):  
Variational Formulation ◽  
Variational Problems ◽  
Nontrivial Solutions ◽  
New Techniques ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Coupled Schrödinger System ◽  
Schrödinger Systems ◽  
Bose Einstein ◽  
Schrödinger System

In this paper, we consider the existence and multiplicity of nontrivial solutions to a quadratically coupled Schrödinger system [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are constants and [Formula: see text], [Formula: see text]. Such type of systems stem from applications in nonlinear optics, Bose–Einstein condensates and plasma physics. The existence (and nonexistence), multiplicity and asymptotic behavior of vector solutions of the system are established via variational methods. In particular, for multiplicity results we develop new techniques for treating variational problems with only partial symmetry for which the classical minimax machinery does not apply directly. For the above system, the variational formulation is only of even symmetry with respect to the first component [Formula: see text] but not with respect to [Formula: see text], and we prove that the number of vector solutions tends to infinity as [Formula: see text] tends to infinity.

EXISTENCE AND MULTIPLICITY OF NONTRIVIAL SOLUTIONS FOR DEGENERATE HEMIVARIATIONAL INEQUALITIES INVOLVING LERAY–LIONS TYPE OPERATOR WITH CRITICAL GROWTH

2013 ◽  
Vol 11 (01) ◽  
pp. 1350007
Author(s):  
KAIMIN TENG
Keyword(s):  
Critical Growth ◽  
Type Operator ◽  
Hemivariational Inequalities ◽  
Concentration Compactness ◽  
Nontrivial Solutions ◽  
Existence And Multiplicity ◽  
Concentration Compactness Principle ◽  
Nonsmooth Critical Point ◽  
Critical Point Theorems ◽  
Compactness Principle

In this paper, we investigate a hemivariational inequality involving Leray–Lions type operator with critical growth. Some existence and multiple results are obtained through using the concentration compactness principle of P. L. Lions and some nonsmooth critical point theorems.

Existence and multiplicity of solutions for discontinuous elliptic problems in ℝ N

2020 ◽  
pp. 1-25
Author(s):  
Claudianor O. Alves ◽  
Ziqing Yuan ◽  
Lihong Huang
Keyword(s):  
Variational Principle ◽  
Variational Methods ◽  
Multiple Solutions ◽  
Elliptic Problems ◽  
Ekeland’S Variational Principle ◽  
Discontinuous Nonlinearity ◽  
Nontrivial Solutions ◽  
Ekeland's Variational Principle ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

Abstract This paper concerns with the existence of multiple solutions for a class of elliptic problems with discontinuous nonlinearity. By using dual variational methods, properties of the Nehari manifolds and Ekeland's variational principle, we show how the ‘shape’ of the graph of the function A affects the number of nontrivial solutions.

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