scholarly journals Existence of solutions for a class of $p(x)$-curl systems arising in electromagnetism without (A-R) type conditions

2020 ◽  
Vol 51 (3) ◽  
pp. 187-200
Author(s):  
Nguyen Thanh Chung
Keyword(s):  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Mountain Pass ◽  
Fountain Theorem ◽  
Multiplicity Results ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

In this paper, we study the existence and multiplicity of solutions for a class of of $p(x)$-curl systems arising in electromagnetism.  Under suitable conditions on the nonlinearities which do not satisfy Ambrosetti-Rabinowitz type conditions, we obtain some existence and multiplicity results for the problem by using the mountain pass theorem and fountain theorem. Our main results in this paper complement and extend some earlier ones concerning the $p(x)$-curl operator in [4, 15].

scholarly journals Existence Results for apx-Kirchhoff-Type Equation without Ambrosetti-Rabinowitz Condition

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Libo Wang ◽  
Minghe Pei
Keyword(s):  
Existence Of Solutions ◽  
Type Equation ◽  
Existence Results ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Infinitely Many Solutions ◽  
Fountain Theorem ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Existence And Multiplicity

We consider the existence and multiplicity of solutions for thepx-Kirchhoff-type equations without Ambrosetti-Rabinowitz condition. Using the Mountain Pass Lemma, the Fountain Theorem, and its dual, the existence of solutions and infinitely many solutions were obtained, respectively.

scholarly journals Multiplicity results for Kirchhoff type elliptic problems with Hardy potential

2019 ◽  
Vol 38 (4) ◽  
pp. 31-50
Author(s):  
M. Bagheri ◽  
Ghasem A. Afrouzi
Keyword(s):  
Local Minimum ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Elliptic Problems ◽  
Mountain Pass ◽  
Hardy Potential ◽  
Multiplicity Results ◽  
Kirchhoff Type ◽  
Minimum Theorem

In this paper, we are concerned with the existence of solutions for fourth-order Kirchhoff type elliptic problems with Hardy potential. In fact, employing a consequence of the local minimum theorem due to Bonanno and mountain pass theorem we look into the existence results for the problem under algebraic conditions with the classical Ambrosetti-Rabinowitz (AR) condition on the nonlinear term. Furthermore, by combining two algebraic conditions on the nonlinear term using two consequences of the local minimum theorem due to Bonanno we ensure the existence of two solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence of third solution for our problem.

scholarly journals Existence and Multiplicity Results of Homoclinic Solutions for the DNLS Equations with Unbounded Potentials

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Defang Ma ◽  
Zhan Zhou
Keyword(s):  
Difference Equations ◽  
Mountain Pass Theorem ◽  
Sufficient Conditions ◽  
Homoclinic Solutions ◽  
Fountain Theorem ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Special Cases ◽  
Discrete Nonlinear Schrödinger Equations ◽  
The Difference

A class of difference equations which include discrete nonlinear Schrödinger equations as special cases are considered. New sufficient conditions of the existence and multiplicity results of homoclinic solutions for the difference equations are obtained by making use of the mountain pass theorem and the fountain theorem, respectively. Recent results in the literature are generalized and greatly improved.

scholarly journals Existence and Multiplicity of Homoclinic Orbits for Second-Order Hamiltonian Systems with Superquadratic Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Ying Lv ◽  
Chun-Lei Tang
Keyword(s):  
Hamiltonian Systems ◽  
Mountain Pass Theorem ◽  
Homoclinic Orbits ◽  
Second Order ◽  
Mountain Pass ◽  
Fountain Theorem ◽  
Existence And Multiplicity ◽  
Second Order Hamiltonian Systems ◽  
Superquadratic Potential

We investigate the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems with local superquadratic potential by using the Mountain Pass Theorem and the Fountain Theorem, respectively.

Solutions of nonlinear problems involving p(x)-Laplacian operator

2015 ◽  
Vol 4 (4) ◽  
pp. 285-293 ◽  
Author(s):  
Zehra Yücedağ
Keyword(s):  
Variational Principle ◽  
Sobolev Space ◽  
Variable Exponent ◽  
Mountain Pass Theorem ◽  
Nonlocal Problem ◽  
Nonlinear Problems ◽  
Mountain Pass ◽  
Laplacian Operator ◽  
Fountain Theorem ◽  
Existence And Multiplicity

AbstractIn the present paper, by using variational principle, we obtain the existence and multiplicity of solutions of a nonlocal problem involving p(x)-Laplacian. The problem is settled in the variable exponent Sobolev space W01,p(x)(Ω), and the main tools are the Mountain-Pass theorem and Fountain theorem.

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 class of Navier boundary $p$-biharmonic problem near resonance

2014 ◽  
Vol 32 (2) ◽  
pp. 83 ◽  
Author(s):  
Mohammed Massar ◽  
EL Miloud Hssini ◽  
Najib Tsouli
Keyword(s):  
Saddle Point ◽  
Point Theorem ◽  
Elliptic Problem ◽  
Weak Solutions ◽  
Mountain Pass Theorem ◽  
Mountain Pass ◽  
Saddle Point Theorem ◽  
Biharmonic Problem ◽  
Existence And Multiplicity ◽  
Near Resonance

This paper studies the existence and multiplicity of weak solutions for the following elliptic problem\\$\Delta(\rho|\Delta u|^{p-2}\Delta u)=\lambda m(x)|u|^{p-2}u+f(x,u)+h(x)$ in $\Omega,$\\$u=\Delta u=0$ on $\partial\Omega.$By using Ekeland's variationalprinciple, Mountain pass theorem and saddle point theorem, theexistence and multiplicity of weak solutions are established.

An Ambrosetti–Prodi-type problem for the (p,q)-Laplacian operator

2019 ◽  
Vol 21 (01) ◽  
pp. 1750067
Author(s):  
Taísa Junges Miotto ◽  
Márcio Luís Miotto
Keyword(s):  
Existence Of Solutions ◽  
Laplacian Operator ◽  
Type Problem ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Continuity Result

This work has objective to obtain results of existence and multiplicity of solutions for an Ambrosetti–Prodi-type problem for the [Formula: see text] operator. Moreover, it was proved a continuity result for the parameter which limits the existence of solutions in relation of the parameter [Formula: see text].

scholarly journals Existence of solutions for a boundary problem involving p(x)-biharmonic operator

2012 ◽  
Vol 31 (1) ◽  
pp. 179 ◽  
Author(s):  
Abdel Rachid El Amrouss ◽  
Anass Ourraoui
Keyword(s):  
Boundary Problem ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Mountain Pass ◽  
Biharmonic Operator ◽  
Technical Approach ◽  
Three Solutions

In this paper, we establish the existence of at least three solutions to a boundary problem involving the p(x)-biharmonic operator. Our technical approach is based on theorem obtained by B. Ricceri's variational principale and local mountain pass theorem without (Palais.Smale) condition.

scholarly journals Elliptic problems in variable exponent spaces

2006 ◽  
Vol 74 (2) ◽  
pp. 197-206 ◽  
Author(s):  
Mihai Mihailescu
Keyword(s):  
Variational Principle ◽  
Nonlinear Elliptic Equation ◽  
Variable Exponent ◽  
Mountain Pass Theorem ◽  
Growth Conditions ◽  
Cylindrical Symmetry ◽  
Multiplicity Results ◽  
Variable Exponent Spaces ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

In this paper we study a nonlinear elliptic equation involving p(x)-growth conditions on a bounded domain having cylindrical symmetry. We establish existence and multiplicity results using as main tools the mountain pass theorem of Ambosetti and Rabinowitz and Ekeland's variational principle.

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