scholarly journals Multiple Solutions for Nonlocal Elliptic Systems Involving p(x)-Biharmonic Operator

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 756
Author(s):  
Qing Miao
Keyword(s):  
Sobolev Space ◽  
Elliptic System ◽  
Multiple Solutions ◽  
Sufficient Conditions ◽  
Elliptic Systems ◽  
Biharmonic Operator ◽  
Variational Theorem ◽  
Variational Structure ◽  
Definition Of

This paper analyzes the nonlocal elliptic system involving the p(x)-biharmonic operator. We give the corresponding variational structure of the problem, and then by means of Ricceri’s Variational theorem and the definition of general Lebesgue-Sobolev space, we obtain sufficient conditions for the infinite solutions to this problem.

scholarly journals Non-existence of ground states for a semilinear elliptic system of Lane-Emden-Fowler type

2013 ◽  
Vol 29 (2) ◽  
pp. 187-193
Author(s):  
MIODRAG IOVANOV ◽  
Keyword(s):  
Elliptic System ◽  
Nonlinear Term ◽  
Sufficient Conditions ◽  
Elliptic Systems ◽  
Aequationes Math ◽  
Radial Solutions ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System ◽  
Positive Radial Solutions ◽  
Radially Symmetric Solutions

We obtain sufficient conditions for the non-existence of positive radially symmetric solutions for a class of Lane, Emden and Fowler elliptic systems. In our result, the nonlinear term it was suggested by the work of [D. O’Regan and H. Wang, Positive radial solutions for p-Laplacian systems, Aequationes Math., 75 (2008) 43–50].

scholarly journals Multiple Solutions for a Nonlocal Elliptic Problem Involving p x , q x -Biharmonic Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Qi Zhang ◽  
Qing Miao
Keyword(s):  
Variational Principle ◽  
Elliptic Problem ◽  
Multiple Solutions ◽  
Sufficient Conditions ◽  
Biharmonic Operator ◽  
Type Problem ◽  
Navier Boundary Conditions ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Kirchhoff Type Problem

In this paper, using the variational principle, the existence and multiplicity of solutions for p x , q x -Kirchhoff type problem with Navier boundary conditions are proved. At the same time, the sufficient conditions for the multiplicity of solutions are obtained.

On the existence of stationary solutions for higher-order p-Kirchhoff problems

2014 ◽  
Vol 16 (05) ◽  
pp. 1450002 ◽  
Author(s):  
Giuseppina Autuori ◽  
Francesca Colasuonno ◽  
Patrizia Pucci
Keyword(s):  
Multiple Solutions ◽  
Eigenvalue Problems ◽  
Sufficient Conditions ◽  
Solution Space ◽  
Main Tool ◽  
Rayleigh Quotient ◽  
Polyharmonic Operator ◽  
Homogeneous Case ◽  
Nonlinear Anal ◽  
Variational Structure

In this paper, we establish the existence of two nontrivial weak solutions of possibly degenerate nonlinear eigenvalue problems involving the p-polyharmonic Kirchhoff operator in bounded domains. The p-polyharmonic operators [Formula: see text] were recently introduced in [F. Colasuonno and P. Pucci, Multiplicity of solutions for p(x)-polyharmonic elliptic Kirchhoff equations, Nonlinear Anal.74 (2011) 5962–5974] for all orders L and independently, in the same volume of the journal, in [V. F. Lubyshev, Multiple solutions of an even-order nonlinear problem with convex-concave nonlinearity, Nonlinear Anal.74 (2011) 1345–1354] only for L even. In Sec. 3, the results are then extended to non-degeneratep(x)-polyharmonic Kirchhoff operators. The main tool of the paper is a three critical points theorem given in [F. Colasuonno, P. Pucci and Cs. Varga, Multiple solutions for an eigenvalue problem involving p-Laplacian type operators, Nonlinear Anal.75 (2012) 4496–4512]. Several useful properties of the underlying functional solution space [Formula: see text], endowed with the natural norm arising from the variational structure of the problem, are also proved both in the homogeneous case p ≡ Const. and in the non-homogeneous case p = p(x). In the latter some sufficient conditions on the variable exponent p are given to prove the positivity of the infimum λ1of the Rayleigh quotient for the p(x)-polyharmonic operator [Formula: see text].

Multiple solutions for a class of (p, q)-gradient elliptic systems via a fibering method

2014 ◽  
Vol 144 (2) ◽  
pp. 363-393 ◽  
Author(s):  
Jean Vélin
Keyword(s):  
Elliptic System ◽  
Multiple Solutions ◽  
Elliptic Systems ◽  
Fibering Method

This paper is devoted to the study of a typical (p, q)-gradient elliptic system. We discuss the existence of multiple non-trivial solutions. More precisely, we establish the existence of three non-trivial solutions, obtained by applying the fibering method introduced by Pohozaev.

scholarly journals A note on the variational structure of an elliptic system involving critical Sobolev exponent

2003 ◽  
Vol 2003 (5) ◽  
pp. 227-241
Author(s):  
Mario Zuluaga
Keyword(s):  
Maximum Principle ◽  
Variational Methods ◽  
Elliptic System ◽  
Elliptic Systems ◽  
Critical Sobolev Exponent ◽  
Growth Conditions ◽  
Scalar Case ◽  
Biharmonic Equations ◽  
Variational Structure ◽  
Sobolev Exponent

We consider an elliptic system involving critical growth conditions. We develop a technique of variational methods for elliptic systems. Using the well-known results of maximum principle for systems developed by Fleckinger et al. (1995), we can find positive solutions. Also, we generalize the systems results obtained (for the scalar case) by Brézis and Nirenberg (1983). Also, we give applications to biharmonic equations.

scholarly journals Multiplicity of Solutions for Perturbed Nonhomogeneous Neumann Problem through Orlicz-Sobolev Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Liu Yang
Keyword(s):  
Sobolev Space ◽  
Variational Methods ◽  
Critical Point ◽  
Neumann Problem ◽  
Sobolev Spaces ◽  
Multiple Solutions ◽  
Sufficient Conditions ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Critical Point Theorems

We investigate the existence of multiple solutions for a class of nonhomogeneous Neumann problem with a perturbed term. By using variational methods and three critical point theorems of B. Ricceri, we establish some new sufficient conditions under which such a problem possesses three solutions in an appropriate Orlicz-Sobolev space.

A Philosophical Analysis To Uncover The Meaning And Terminology Of Person In Indonesian Criminal Law Context

2017 ◽  
Vol 1 (1) ◽  
pp. 56
Author(s):  
Nani Mulyati ◽  
Topo Santoso ◽  
Elwi Danil
Keyword(s):  
Criminal Law ◽  
Sufficient Conditions ◽  
Criminal Code ◽  
Legal Person ◽  
Philosophical Approach ◽  
Legal Personality ◽  
Legal Subject ◽  
Long Time ◽  
Definition Of ◽  
Broad Meaning

The definition of person and non-person always change through legal history. Long time ago, law did not recognize the personality of slaves. Recently, it accepted non-human legal subject as legitimate person before the law. This article examines sufficient conditions for being person in the eye of law according to its particular purposes, and then, analyses the meaning of legal person in criminal law. In order to do that, scientific methodology that is adopted in this research is doctrinal legal research combined with philosophical approach. Some theories regarding person and legal person were analysed, and then the concept of person was associated with the accepted definition of legal person that is adopted in the latest Indonesian drafted criminal code. From the study that has been done, can be construed that person in criminal law concerned with norm adressat of the rule, as the author of the acts or omissions, and not merely the holder of rights. It has to be someone or something with the ability to think rationally and the ability to be responsible for the choices he/she made. Drafted penal code embraces human and corporation as its norm adressat. Corporation defined with broad meaning of collectives. Consequently, it will include not only entities with legal personality, but also associations without legal personality. Furthermore, it may also hold all kind of collective namely states, states bodies, political parties, state’s corporation, be criminally liable.

scholarly journals Lyapunov Functions and Lipschitz Stability for Riemann–Liouville Non-Instantaneous Impulsive Fractional Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 730
Author(s):  
Ravi Agarwal ◽  
Snezhana Hristova ◽  
Donal O’Regan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Initial Time ◽  
Lipschitz Stability ◽  
Comparison Results ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Definition Of

In this paper a system of nonlinear Riemann–Liouville fractional differential equations with non-instantaneous impulses is studied. We consider a Riemann–Liouville fractional derivative with a changeable lower limit at each stop point of the action of the impulses. In this case the solution has a singularity at the initial time and any stop time point of the impulses. This leads to an appropriate definition of both the initial condition and the non-instantaneous impulsive conditions. A generalization of the classical Lipschitz stability is defined and studied for the given system. Two types of derivatives of the applied Lyapunov functions among the Riemann–Liouville fractional differential equations with non-instantaneous impulses are applied. Several sufficient conditions for the defined stability are obtained. Some comparison results are obtained. Several examples illustrate the theoretical results.

scholarly journals Multiple solutions of fourth-order difference equations with different boundary conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yuhua Long ◽  
Shaohong Wang ◽  
Jiali Chen
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Difference Equations ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Sufficient Conditions ◽  
Dirichlet Boundary Conditions ◽  
Invariant Sets ◽  
Mountain Pass Lemma ◽  
Order Difference

Abstract In the present paper, a class of fourth-order nonlinear difference equations with Dirichlet boundary conditions or periodic boundary conditions are considered. Based on the invariant sets of descending flow in combination with the mountain pass lemma, we establish a series of sufficient conditions on the existence of multiple solutions for these boundary value problems. In addition, some examples are provided to demonstrate the applicability of our results.

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