Results 91 to 100 of about 2,807 (153)

Anti-selfdual Lagrangians: Variational resolutions of non self-adjoint equations and dissipative evolutions

, 2004
We develop the concept and the calculus of anti-self dual (ASD) Lagrangians which seems inherent to many questions in mathematical physics, geometry, and differential equations. They are natural extensions of gradients of convex functions --hence of self-
Ghoussoub, Nassif
core   +4 more sources

Existence of Exponential p-Stability Nonconstant Equilibrium of Markovian Jumping Nonlinear Diffusion Equations via Ekeland Variational Principle

Advances in Mathematical Physics, 2015
The authors obtained a delay-dependent exponential p-stability criterion for a class of Markovian jumping nonlinear diffusion equations by employing the Lyapunov stability theory and some variational methods.
Ruofeng Rao, Shouming Zhong
doaj   +1 more source

Perturbed subcritical Dirichlet problems with variable exponents

Electronic Journal of Differential Equations, 2016
We study a class of nonhomogeneous elliptic problems with Dirichlet boundary condition and involving the p(x)-Laplace operator and power-type nonlinear terms with variable exponent.
Ramzi Alsaedi
doaj  

Multiple positive solutions for biharmonic equation of Kirchhoff type involving concave-convex nonlinearities

Electronic Journal of Differential Equations, 2020
In this article, we study the multiplicity of positive solutions for the biharmonic equation of Kirchhoff type involving concave-convex nonlinearities, $$ \Delta^2u-\Big(a+b\int_{\mathbb{R}^N}|\nabla u|^2dx\Big)\Delta u+V(x)u =\lambda f_1(x)|u|^{q-2 ...
Fengjuan Meng, Fubao Zhang, Yuanyuan Zhang   +2 more
doaj  

Multiple solutions for nonlinear discontinuous strongly resonant elliptic problems

Abstract and Applied Analysis, 2000
We consider quasilinear strongly resonant problems with discontinuous right-hand side. To develop an existence theory we pass to a multivalued problem by, roughly speaking, filling in the gaps at the discontinuity points.
Nikolaos C. Kourogenis, Nikolaos S. Papageorgiou   +1 more
doaj   +1 more source

Existence of nontrivial solutions for a fractional p & q $p\&q$ -Laplacian equation with sandwich-type and sign-changing nonlinearities

Journal of Inequalities and Applications
In this paper, we deal with the following fractional p & q $p\&q$ -Laplacian problem: { ( − Δ ) p s u + ( − Δ ) q s u = λ a ( x ) | u | θ − 2 u + μ b ( x ) | u | r − 2 u in Ω , u ( x ) = 0 in R N ∖ Ω , $$ \left \{ \textstyle\begin{array}{l@{\quad }l ...
Qin Li, Zonghu Xiu, Lin Chen
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Fixed-Point Results and the Ekeland Variational Principle in Vector B-Metric Spaces

Axioms
In this paper, we extend the concept of b-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results analogous to those in the
Radu Precup, Andrei Stan
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A generalization of the Ekeland variational principle

, 2020
In this short communication, we present a generalization of the Ekeland variational principle. The main result is established through standard tools of functional analysis and calculus of variations. The novelty here is a result involving the second G teaux variation of the functional in question.
openaire   +2 more sources

Multiple positive solutions for Kirchhoff type problems involving concave and convex nonlinearities in R^3

Electronic Journal of Differential Equations, 2016
In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover ...
Xiaofei Cao, Junxiang Xu, Jun Wang
doaj  

Completeness in quasi-metric spaces and Ekeland Variational Principle

Topology and its Applications, 2011
The author establishes a quasi-metric version of the Ekeland variational principle and studies its connections with the completeness properties of the underlying quasi-metric space. The equivalence with Caristi-Kirk's fixed point theorem and a proof of Clarke's fixed point theorem for directional contractions within this framework are also investigated.
openaire   +1 more source