High energy solutions of modified quasilinear fourth-order elliptic equation

Abstract

This paper focuses on the following modified quasilinear fourth-order elliptic equation:where 2 = ( ) is the biharmonic operator, a > 0, b ≥ 0, λ ≥ 1 is a parameter,

Fixed Point Theory and Positive Solutions for a Ratio-Dependent Elliptic System

“…We remark that problem (1) with homogeneous Neumann boundary condition was discussed in [6]. We will consider what is more general in this paper, where the parameters , are positive and ∈ R. What is more, since (1) comes from the biological module, our results and methods are different from those in [13][14][15][16] and references therein, which are also the Dirichlet boundary problems.…”

An exact estimate result for p-biharmonic equations with Hardy potential and negative exponents

“…Biharmonic equations describe the sport of a rigid body and the deformations of an elastic beam. For example, this type of equation provides a model for considering traveling wave in suspension bridges [5,16,27,30,36]. Various methods and tools have been adopted to deal with singular problems, such that fixed point theorems [14], topological methods [37], Fourier and Laurent transformation [18,19], monotone iterative methods [21], global bifurcation theory [12], and degree theory [22,31].…”