Abstract
Aims/ Objectives: In this paper, we study the Monge-Amp`ere type equation det D2u + α∆u = p(|x|)f(u)(x ∈ Rn). 
 In the previous articles, the equation with Monge-Amp`ere operator or Laplace operator has been studied extensively. However, the research about the combination of two kinds of operator is scarce. We would like do some research on this topic. We obtain a sufficient condition of the existence of entire positive solutions for the equation. 
 Study Design: Study on the existence of solutions. 
 Place and Duration of Study: Department of Mathematics and Physics, North China Electric Power University, September 2019 to present. 
 Methodology: We prove the existence of the solution by constructing Euler’s break line, combining the idea of transformation and the method of mathematical analysis. Results: We obtain a sufficient condition of the existence of entire positive solutions for the equation.
 Conclusion: We prove the existence of entire positive solutions to Monge-Amp`ere type equation det D2u + α∆u = p(|x|)f(u)(x ∈ Rn) and obtain the sufficient condition for the existence of solutions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
