Bubbling Phenomena of Certain Palais-Smale Sequences of m-Harmonic Type Systems
, 2008 . In this paper, we study the bubbling phenomena of weak solution sequences of a class of degenerate quasilinear elliptic systems of m-harmonic type. We prove that, under appropriate conditions, the energy is preserved during the bubbling process.
Changyou Wang, Libin Mou
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Nonlinear elliptic systems with exponential nonlinearities
Electronic Journal of Differential Equations, 2002 In this paper we investigate the existence of solutions for {gather*} -mathop{m div}( a(| abla u | ^N)| abla u |^{N-2}u ) = f(x,u,v) quad mbox{in } Omega -mathop{m div}(a(| abla v| ^N)| abla v |^{N-2}v )= g(x,u,v) quad mbox{in } Omega u(x) = v(x) = 0 ...
Said El Manouni, Abdelfattah Touzani
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A Linear Perturbed Palais-Smale Condition for Lower Semicontinuous Functions on Banach Spaces [PDF]
, 2007 本文首先回顾了变分原理，最优化，扰动优化，扰动强优化和P-S条件发展的历史过程，从而自然引入了线性扰动P-S条件的概念。接着对本文所要用到的基本概念作了一个简单的介绍，最后通过强暴露点，强暴露泛函和非凸函数凸化的方法给出了本文主要定理的证明。 主要结果如下：1.举例说明了线性扰动P-S条件严格弱于P-S条件；2.给出了定义在具有RNP的Banach空间上有下界的下半连续函数的线性扰动P-S条件成立的特征条件。In this paper, we discuss linear perturbed ...
左麦芳
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Multiplicity of solutions for a class of elliptic systems in $R^N$
Electronic Journal of Differential Equations, 2006 This article concerns the multiplicity of solutions for the system of equations $$displaylines{ -Delta u + V(epsilon x)u = alpha |u|^{alpha-2}u|v|^{eta}, cr -Delta v + V(epsilon x)v = eta |u|^{alpha}|v|^{eta-2}v }$$ in $mathbb{R}^N$, where $V$ is a ...
Giovany M. Figueiredo
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Standing Waves of the NLS Equation on Locally Finite Weighted Graphs: A Linking Geometry Approach
Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri DergisiWe investigate wave solutions of the nonlinear Schrödinger equation (H-λ)u=f(x,u) on a locally finite weighted graph, where H is the associated Schrödinger operator.
Setenay Akduman
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On the Palais-Smale condition in geometric knot theory
We prove that various families of energies relevant in geometric knot theory satisfy the Palais-Smale condition (PS) on submanifolds of arclength para\-metrized knots. These energies include linear combinations of the Euler-Bernoulli bending energy with a wide variety of non-local knot energies, such as O'Hara's self-repulsive potentials $E^{α,p}
Freches, Nicolas +3 more
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Spectrum of a Self-Adjoint Operator and Palais-Smale Conditions [PDF]
, 2017 The spectrum and essential spectrum of a self-adjoint operator in a real Hilbert space are characterized in terms of Palais-Smale conditions on its quadratic form and Rayleigh quotient ...
Stuart, C. A.
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On the Evolution of Regularized Dirac-Harmonic Maps from Closed Surfaces. [PDF]
Results Math, 2020 Branding V.
europepmc +1 more source
Solutions to perturbed eigenvalue problems of the p-Laplacian in RN
Electronic Journal of Differential Equations, 1997 Using a variational approach, we investigate the existence of solutions for non-autonomous perturbations of the p-Laplacian eigenvalue problem $$ -Delta _pu=f(x,u)quad { m in}quad {Bbb R}^N,. $$ Under the assumptions that the primitive $F(x,u)$ of $f(x,u)
Joao Marcos Do O
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Infinitely Many Solutions for Schrödinger–Poisson Systems and Schrödinger–Kirchhoff Equations
MathematicsBy applying Clark’s theorem as altered by Liu and Wang and the truncation method, we obtain a sequence of solutions for a Schrödinger–Poisson system −Δu+V(x)u+ϕu=f(u)inR3,−Δϕ=u2inR3 with negative energy.
Shibo Liu
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