Results 71 to 80 of about 869,106 (168)

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
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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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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
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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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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
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Mountain pass frozen planet orbits in the helium atom model [PDF]

We seek frozen planet orbits for the helium atom through an application of the Mountain Pass Lemma to the Lagrangian action functional. Our method applies to a wide class of gravitational-like interaction potentials thus generalising the results in [7 ...
Terracini, Susanna, Canneori, Gian Marco, Baranzini, Stefano   +2 more
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Critical singular problems via concentration-compactness lemma [PDF]

, 2007
In this work we consider existence and multiplicity results of nontrivial solutions for a class of quasilinear degenerate elliptic equations in RN of the form(P)−div[|x|−ap|∇u|p−2∇u]+λ|x|−(a+1)p|u|p−2u=|x|−bq|u|q−2u+f, where x∈RN ...
Carrião, Paulo Cesar, Miyagaki, Olimpio Hiroshi, Assunção, Ronaldo B.   +2 more
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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
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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
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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
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