Existence and Multiplicity of a Nonhomogeneous Polyharmonic Equation With Critical Exponential Growth in Even Dimension

2015/04/13 by Abhishek Sarkar, Sarkar, Abhishek
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1504.03267

arxiv created 2015/04/13 · openalex publication_date 2015/04/13 · arxiv updated 2015/04/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we study the existence of at least two positive weak solutions for an inhomogeneous fourth order equation with Navier boundary data involving nonlinearities of critical growth with a bifurcation parameter λ in ℝ^2m. We establish here the lower and upper bound for λ which determine multiplicity and non-existence respectively.

Related

• New type of solutions for the critical polyharmonic equation
• Existence and stability properties of entire solutions to the polyharmonic equation (-Δ)^m u=e^u for any m≥ 1
• Polyharmonic Kirchhoff type equations with singular exponential nonlinearities
• Existence and local uniqueness of bubbling solutions for poly-harmonic equations with critical growth
• Normalized solutions to polyharmonic equations with Hardy-type potentials and exponential critical nonlinearities