Article
Mathematics
Rui Yang, Jong Kyu Lee, Yong-Hoon Lee
Summary: This paper presents an existence theorem for positive solutions to the Dirichlet boundary value problem of one-dimensional Minkowski curvature equations. The theorem is applied to investigate a constructive method for determining the numerical range of parameters where positive solutions exist. Additionally, a nonexistence theorem for positive solutions is established for the corresponding one-parameter family of problems. The main argument for the proof of the existence theorem utilizes Krasnoselskii's theorem of cone expansion and compression. A numerical algorithm and various examples are provided to illustrate numerical information about the ranges of existence and nonexistence parameters, which have previously only been discussed in a theoretical manner.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2022)
Article
Mathematics, Applied
Yibin Feng, Shengnan Hu, Weiru Liu
Summary: This paper studies the existence and uniqueness of solutions to the Orlicz Aleksandrov problem for non-symmetric measures, including the existence with p > 0 and uniqueness with p >= 1 of solutions to the L-p Aleksandrov problem.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Zhongzi Zhao, Ruyun Ma, Yan Zhu
Summary: We investigate discrete periodic problems with Minkowski-curvature operator and prove that the problem has multiple odd sign-changing solutions and multiple even sign-changing solutions when g(t, .) is odd.
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Tingzhi Cheng, Xianghui Xu
Summary: In this paper, the existence of positive solutions for the one-dimensional Minkowski curvature problem with either singular weight function or singular nonlinear term is considered. By using fixed point arguments and perturbation technique, new existence results of positive solutions are established under different assumptions on the nonlinear term. Moreover, some examples are given as applications.
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Xingchen Yu, Shiping Lu, Fanchao Kong
Summary: This paper studies the existence, non-existence, and multiplicity of positive periodic solutions to a class of Minkowski-curvature equations with indefinite attractive singularities. A multiplicity result of Ambrosetti-Prodi type is established using a new method of construction of lower functions and some properties of Leray-Schauder degree.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics
Mohammad N. Ivaki, Emanuel Milman
Summary: By employing the local version of the Brunn-Minkowski inequality, this study provides a new and simple proof of a significant result in the field of Gauss curvature flow. The authors also extend the result to various nonlinear problems and establish that origin-centred balls are the unique solutions to a class of Christoffel-Minkowski type problems.
ADVANCES IN MATHEMATICS
(2023)
Article
Mathematics, Applied
Zhiqian He, Liangying Miao
Summary: In this paper, the Dirichlet problem of quasilinear differential system with mean curvature operator in Minkowski space is considered in a ball in R-N. By utilizing Leggett-Williams' fixed point theorem, the existence of three positive radial solutions is obtained for this system with Lane-Emden type nonlinearities in a superlinear case.
Article
Mathematics
Li Chen, YanNan Liu, Jian Lu, Ni Xiang
Summary: This paper studies the dual Orlicz-Minkowski problem and obtains a new existence result for smooth even solutions by considering a geometric flow involving Gauss curvature and functions of normal vectors and radial vectors.
JOURNAL OF GEOMETRIC ANALYSIS
(2022)
Article
Operations Research & Management Science
Rafal Kamocki
Summary: This paper discusses optimal control problems involving ordinary control systems, linear control variables, fractional Dirichlet and Dirichlet-Neumann Laplace operators, and a nonlinear integral performance index. The main result is a theorem on the existence of optimal solutions for such problems, utilizing a characterization of weak lower semicontinuity of integral functionals.
OPTIMIZATION LETTERS
(2021)
Article
Mathematics, Applied
Alberto Boscaggin, Guglielmo Feltrin, Fabio Zanolin
Summary: We investigate the existence of positive solutions for a class of Minkowski-curvature equations with indefinite weight and nonlinear term. As an example, we prove the existence of a positive solution for both periodic and Neumann boundary conditions by using a topological degree technique.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2023)
Article
Mathematics, Applied
Jie Yang, Guoping Chen
Summary: The paper investigates the existence of solutions for impulsive mixed boundary value problems involving Caputo fractional derivatives, with conclusions drawn from Krasnoselskii's fixed point theorem and Arzela-Ascoli theorem. Several examples are provided to illustrate the main results obtained.
Article
Mathematics
Csaba Farkas, Patrick Winkert
Summary: This paper investigates a class of singular double phase problems on Minkowski spaces using Finsler manifolds, allowing certain critical growth for the right-hand sides. By employing variational tools under general assumptions, the existence of at least one non-trivial weak solution for such a problem is proven. This marks the first work dealing with a Finsler double phase operator, even in the nonsingular case.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics
Rui Niu, Tianxing Wu
Summary: In this article, the study of Kirchhoff-Choquard equations is presented. It is proved that for sufficiently small parameter A, the equations have mountain pass, least energy, and ground state solutions by using variational methods and establishing subtle inequalities.
Article
Mathematics
Julian Lopez-Gomez, Pierpaolo Omari
Summary: The aim of this paper is to analyze the existence, multiplicity, and regularity issues of positive solutions for the quasilinear Neumann problem. Depending on the behavior of the potential function F(u) at different points and the weight function a(x) at its nodal points, the manifold patterns of these solutions are discussed.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Zhiqian He, Liangying Miao
Summary: This paper investigates the existence of S-shaped connected component of positive radial solutions for the Dirichlet problem with mean curvature operator in Minkowski space. By bifurcation technique, the existence and multiplicity of positive radial solutions are shown for bifurcation parameter lying in various intervals.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2022)
