Ground state solutions and multiple positive solutions for nonhomogeneous Kirchhoff equation with Berestycki-Lions type conditions

Abstract

This article is concerned with the following Kirchhoff equation: −a+b∫R3∣∇u∣2dxΔu=g(u)+h(x)inR3,-\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}{| \nabla u| }^{2}{\rm{d}}x\right)\Delta u=g\left(u)+h\left(x)\hspace{1em}{\rm{in}}\hspace{0.33em}{{\mathbb{R}}}^{3}, where aa and bb are positive constants and h≠0h\ne 0. Under the Berestycki-Lions type conditions on gg, we prove that the equation has at least two positive solutions by using variational methods. Furthermore, we obtain the existence of ground state solutions.

Keywords

• nonhomogeneous kirchhoff equation
• variational methods
• berestycki-lions type conditions
• multiple positive solutions
• ground state solutions
• 35a16
• 35b09
• 35b32
• 35j20
• 35j60