Results 51 to 60 of about 144 (97)

A generalization of Ekeland's variational principle with applications

Electronic Journal of Differential Equations, 2006
In this paper, we establish a variant of Ekeland's variational principle. This result suggest to introduce a generalization of the famous Palais-Smale condition.
Abdel R. El Amrouss, Najib Tsouli
doaj  

Eigenvalues for a Neumann Boundary Problem Involving the p(x)-Laplacian

Advances in Mathematical Physics, 2015
We study the existence of weak solutions to the following Neumann problem involving the p(x)-Laplacian operator:  -Δp(x)u+e(x)|u|p(x)-2u=λa(x)f(u), in  Ω, ∂u/∂ν=0, on  ∂Ω.
Qing Miao
doaj   +1 more source

Ekeland’s Variational Principle and Minimization Takahashi’s Theorem in Generalized Metric Spaces

Mathematics, 2018
We consider a distance function on generalized metric spaces and we get a generalization of Ekeland Variational Principle (EVP). Next, we prove that EVP is equivalent to Caristi–Kirk fixed point theorem and minimization Takahashi’s theorem.
Eshagh Hashemi, Reza Saadati
doaj   +1 more source

Concerning Kirk’s problem

Fixed Point Theory and Algorithms for Sciences and Engineering
This paper presents a straightforward statement for Khamsi’s theorem without assuming continuity or nondecreasing restrictions on η. Additionally, a new proof provides an affirmative answer to Kirk’s problem, supported by examples.
Hamid Mottaghi Golshan
doaj   +1 more source

Maximum principle for a nonlinear size-structured model of fish and fry management

Nonlinear Analysis, 2018
This paper investigates the maximum principle for a nonlinear size-structured model that describes the optimal management of the fish resources taking into account harvesting the fish and putting the fry.
Rong Liu, Guirong Liu
doaj   +1 more source

Existence and multiplicity of weak solutions for a class of degenerate nonlinear elliptic equations

Boundary Value Problems, 2006
The goal of this paper is to study the existence and the multiplicity of non-trivial weak solutions for some degenerate nonlinear elliptic equations on the whole space RN. The solutions will be obtained in a subspace of the Sobolev space W1/p(RN).
Mihai Mihăilescu
doaj   +1 more source

An order drop theorem

Le Matematiche, 2006
A drop theorem on ordered metric spaces is established from the (pre) order version of Ekeland’s variational principle in Turinici [An St UAIC Ia (Math), 36 (1990), 329-352]. The logical equivalence between these results is also discussed.
Mihai Turinici
doaj  

Modern perspectives in Proof Theory. [PDF]

Philos Trans A Math Phys Eng Sci, 2023
Aguilera JP, Pakhomov F, Weiermann A.
europepmc   +1 more source

Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3

Abstract and Applied Analysis, 2014
We study the following nonhomogeneous Kirchhoff equation: -(a+b∫R3‍|∇u|2dx)Δu+u=k(x)f(u)+h(x),  x∈R3,  u∈H1(R3),  u>0,  x∈R3, where f is asymptotically linear with respect to t at infinity.
Ling Ding, Lin Li, Jin-Ling Zhang
doaj   +1 more source

Multiplicity Results for Variable-Order Nonlinear Fractional Magnetic Schrödinger Equation with Variable Growth

Journal of Function Spaces, 2020
In this paper, we prove the multiplicity of nontrivial solutions for a class of fractional-order elliptic equation with magnetic field. Under appropriate assumptions, firstly, we prove that the system has at least two different solutions by applying the ...
Jianwen Zhou, Bianxiang Zhou, Yanning Wang   +2 more
doaj   +1 more source