Yue, Xu Xiaoling, Han
Published in
Open Mathematics

In this paper, we use the shooting method to study the solvability of the boundary value problem of differential equations with sign-changing weight function: u ″ ( t ) + ( λ a + ( t ) − μ a − ( t ) ) g ( u ) = 0 , 0 0 g\left(s)\gt 0 for s ∈ ( 0 , 1 ) s\in \left(0,1) , g ( s )

Wang, Youyu Huang, Yue Li, Xianfei
Published in
Demonstratio Mathematica

By using the theory of fixed point index and spectral theory of linear operators, we study the existence of positive solutions for Riemann-Liouville fractional differential equations at resonance. Our approach will provide some new ideas for the study of this kind of problem.

Lyons, Tony
Published in
Journal of Mathematical Fluid Mechanics

We generate explicit height-dependent eddy viscosity coefficients in the Ekman layer from convex wind speed profiles. The solutions we obtain are parameterized in terms of the relative deflection angle between the wind directions at the top and bottom of the flow, as well as the geostrophic wind speed and a velocity scale we interpret as the transf...

Babajanov, Bazar Abdikarimov, Fakhriddin
Published in
Frontiers in Applied Mathematics and Statistics

In this article, we construct exact traveling wave solutions of the loaded Korteweg-de Vries, the loaded modified Korteweg-de Vries, and the loaded Gardner equation by the functional variable method. The performance of this method is reliable and effective and gives the exact solitary and periodic wave solutions. All solutions to these equations ha...

AhmadSoltani, Leyla
Published in
Nonlinear Engineering

This work presents the existential and unique results for the solution to a kind of high-order fractional nonlinear differential equations involving Caputo fractional derivative. The boundary condition is of the integral type, which entangles both starting and ending points of the domain. First, the unique exact solution is extracted in terms of Gr...

Long, Yuhua
Published in
Advances in Nonlinear Analysis

In this article, we study discrete Kirchhoff-type problems when the nonlinearity is resonant at both zero and infinity. We establish a series of results on the existence of nontrivial solutions by combining variational method with Morse theory. Several examples are provided to illustrate applications of our results.

Li, Gang
Published in
Calculus of Variations and Partial Differential Equations

In this paper we show that for a generalized Berger metric g^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{g}}$$\end{document} on S3\documentclass[12pt]{minimal...

Fencl, M López-Gómez, J
Published in
Nonlinearity

This paper analyzes the structure of the set of positive solutions of a class of one-dimensional superlinear indefinite bvp’s. It is a paradigm of how mathematical analysis aids the numerical study of a problem, whereas simultaneously its numerical study confirms and illuminates the analysis. On the analytical side, we establish the fast decay of t...

Hai, D. D. Wang, X.
Published in
Mediterranean Journal of Mathematics

We prove the existence, nonexistence and multiplicity of positive solution to the problem -(ϕ(u′))′=λh(t)f(u),0

Fenucci, M.
Published in
Partial Differential Equations and Applications

We first take into account variational problems with periodic boundary conditions, and briefly recall some sufficient conditions for a periodic solution of the Euler–Lagrange equation to be either a directional, a weak, or a strong local minimizer. We then apply the theory to circular orbits of the Kepler problem with potentials of type 1/rα,α>0\do...