Infinitely many radial solutions of superlinear elliptic problems with dependence on the gradient terms in an annulus

Abstract

Abstract In this paper, we are concerned with elliptic problems { − Δ u = f ( u ) + g ( | x | , u , x | x | ⋅ ∇ u ) , x ∈ Ω , u | ∂ Ω = 0 , $$ \textstyle\begin{cases} -\Delta u= f(u)+ g( \vert x \vert ,u,\frac{x}{ \vert x \vert }\cdot \nabla u),&x\in \Omega , \\ u|_{\partial \Omega}=0, \end{cases} $$ where Ω = { x ∈ R N : R 1 2 $N>2$ , 0 0 $C>0$ , 0 < β < 1 4 ( R 2 − R 1 ) 2 $0<\beta < \frac{1}{4(R_{2}-R_{1})^{2}}$ . We obtain infinitely many radial solutions with prescribed nodal properties using bifurcation techniques.

Keywords

• Elliptic problems
• Superlinear problem
• Nodal solutions
• Bifurcation
• Annulus