Positive radial solutions to a ‘semilinear’ equation involving the Pucci's operator

AbstractIn this article we prove existence of positive radially symmetric solutions for the nonlinear elliptic equationMλ,Λ+(D2u)−γu+f(u)=0inBR,u=0on∂BR,where Mλ,Λ+ denotes the Pucci's extremal operator with parameters 0<λ⩽Λ and BR is the ball of radius R in RN, N⩾3. The result applies to a wide class of nonlinear functions f, including the important model cases: (i) γ=1 and f(s)=sp, 1<p<p∗+. (ii) γ=0, f(s)=αs+sp, 1<p<p∗+ and 0⩽α<μ1+. Here p∗+ is critical exponent for Mλ,Λ+ and μ1+ is the first eigenvalue of Mλ,Λ+ in BR. Analogous results are obtained for the operator Mλ,Λ−