Asymptotic Behavior of Ground State Solutions of Some Combined Nonlinear Problems

Positive solutions with specific asymptotic behavior for a polyharmonic problem on Rn

“…In this work, we generalize the results of [4] to equation (1.1). Note that the sub and supersolution method is not available for (1.1).…”

“…In particular, many authors studied the exact asymptotic behavior of solutions of equation (1.2), see for example [4-6, 10, 12, 13, 15, 16, 21]. For instance in [4], the authors studied (1.2) in R n (n ≥ 3). Thanks to the sub and supersolution method, they showed that equation (1.2) has a unique positive classical solution which satisfies homogeneous Dirichlet boundary conditions.…”

“…We note that (1.1) is formally equivalent to the integral equation 4) and u = V m,n (a) is a solution in the linear case with α = 0. The asymptotic behavior of V m,n (a) is similar to that of a itself, only with different λ and L (Proposition 2.4).…”