1
|
A Mosquito Population Suppression Model by Releasing Wolbachia-Infected Males. Bull Math Biol 2022; 84:121. [DOI: 10.1007/s11538-022-01073-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2021] [Accepted: 08/29/2022] [Indexed: 11/02/2022]
|
2
|
Infinitely Many Solutions for the Discrete Boundary Value Problems of the Kirchhoff Type. Symmetry (Basel) 2022. [DOI: 10.3390/sym14091844] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this paper, we study the existence and multiplicity of solutions for the discrete Dirichlet boundary value problem of the Kirchhoff type, which has a symmetric structure. By using the critical point theory, we establish the existence of infinitely many solutions under appropriate assumptions on the nonlinear term. Moreover, we obtain the existence of infinitely many positive solutions via the strong maximum principle. Finally, we take two examples to verify our results.
Collapse
|
3
|
Infinite Homoclinic Solutions of the Discrete Partial Mean Curvature Problem with Unbounded Potential. MATHEMATICS 2022. [DOI: 10.3390/math10091436] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/10/2022]
Abstract
The mean curvature problem is an important class of problems in mathematics and physics. We consider the existence of homoclinic solutions to a discrete partial mean curvature problem, which is tied to the existence of discrete solitons. Under the assumptions that the potential function is unbounded and that the nonlinear term is superlinear at infinity, we obtain the existence of infinitely many homoclinic solutions to this problem by means of the fountain theorem in the critical point theory. In the end, an example is given to illustrate the applicability of our results.
Collapse
|