Results 61 to 70 of about 247 (144)

Multiplicity of solutions to the sum of polyharmonic equations with critical Sobolev exponents

Electronic Journal of Differential Equations, 2015
In this article, we prove multiplicity of solutions for the sum of polyharmonic equation with critical Sobolev exponent. The proof is based upon the methods of weakly lower semi-continuous of the functionals and the Mountain Pass Lemma without (PS ...
Wei Liu, Gao Jia, Lu-Quian Guo
doaj  

Multiple Solutions of a Nonlocal Problem with Nonlinear Boundary Conditions

Discrete Dynamics in Nature and Society
In this article, we consider a class of nonlocal p(x)-Laplace equations with nonlinear boundary conditions. When the nonlinear boundary involves critical exponents, using the concentration compactness principle, mountain pass lemma, and fountain theorem,
Jie Liu, Qing Miao
doaj   +1 more source

Periodic Solutions of a Class of Fourth-Order Superlinear Differential Equations

Abstract and Applied Analysis, 2012
This paper deals with the periodic solutions of a class of fourth-order superlinear differential equations. By using the classical variational techniques and symmetric mountain pass lemma, the periodic solutions of a single equation in literature are ...
Yanyan Li, Yuhua Long
doaj   +1 more source

Boundary Value Problems for Fourth Order Nonlinear p-Laplacian Difference Equations

Journal of Applied Mathematics, 2014
We consider the boundary value problem for a fourth order nonlinear p-Laplacian difference equation containing both advance and retardation. By using Mountain pass lemma and some established inequalities, sufficient conditions of the existence of ...
Qinqin Zhang
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Infinitely many solutions for a class of hemivariational inequalities involving p(x)-Laplacian

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017
In this paper hemivariational inequality with nonhomogeneous Neumann boundary condition is investigated. The existence of infinitely many small solutions involving a class of p(x) - Laplacian equation in a smooth bounded domain is established.
Fattahi Fariba, Alimohammady Mohsen
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Du Bois-Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)-Laplacian on a Bounded Time Scale. [PDF]

Entropy (Basel), 2021
Mawhin J, Skrzypek E, Szymańska-Dȩbowska K.   +2 more
europepmc   +1 more source

Characterization of solutions to equations involving the p(x)-Laplace operator

Electronic Journal of Differential Equations, 2017
In this article we study two problems, a nonlinear eigenvalue problem involving the p(x)-Laplacian and a subcritical boundary value problem for the same operator.
Iulia Dorotheea Stircu, Vasile Florin Uta   +1 more
doaj  

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

Boundary Value Problems, 2019
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
Yuhua Long, Shaohong Wang, Jiali Chen
doaj   +1 more source

Nonhomogeneous elliptic problems of Kirchhoff type involving critical Sobolev exponents

Electronic Journal of Differential Equations, 2015
This article concerns the existence and the multiplicity of solutions for nonhomogeneous elliptic Kirchhoff problems involving the critical Sobolev exponent, defined on a regular bounded domain of $\mathbb{R}^3$.
Safia Benmansour, Mohammed Bouchekif
doaj  

Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term

Journal of Applied Mathematics, 2012
We study the following fourth-order elliptic equations: Δ2𝑢+𝑎Δ𝑢=𝑓(𝑥,𝑢),𝑥∈Ω,𝑢=Δ𝑢=0,𝑥∈𝜕Ω, where Ω⊂ℝ𝑁 is a bounded domain with smooth boundary 𝜕Ω and 𝑓(𝑥,𝑢) is asymptotically linear with respect to 𝑢 at infinity.
Qiong Liu, Dengfeng Lü
doaj   +1 more source