In this paper, we are concerned with positive entire solutions to elliptic equations of the form Δu+ f(x,u)= 0 x∈ RN N ≥ 3 where u →f(x,u) is not assumed to be regular near u = 0 and f(x,u) may be more general in...In this paper, we are concerned with positive entire solutions to elliptic equations of the form Δu+ f(x,u)= 0 x∈ RN N ≥ 3 where u →f(x,u) is not assumed to be regular near u = 0 and f(x,u) may be more general involving both singular and sublinear terms. Some sufficient conditions are given with the aid of the barrier method and ODE approach, which guarantee the existence of positive entire solutions that tend to any sufficiently large constants arbitrarily prescribed in advance.展开更多
A class of singularly perturbed problems for the nonlinear elliptic equations is considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the boundar...A class of singularly perturbed problems for the nonlinear elliptic equations is considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems are studied, which reduced equations possess two intersecting solutions.展开更多
The singularly perturbed problems for the nonlinear elliptic systems in the half space are considered. Under suitable conditions, using the comparison theorem the existence and asymptotic behavior of solution for the ...The singularly perturbed problems for the nonlinear elliptic systems in the half space are considered. Under suitable conditions, using the comparison theorem the existence and asymptotic behavior of solution for the boundary value problem are studied.展开更多
The authors consider the existence of singular limit solutions for a family of nonlinear elliptic problems with exponentially dominated nonlinearity and Dirichlet boundary condition and generalize the results of [3].
文摘In this paper, we are concerned with positive entire solutions to elliptic equations of the form Δu+ f(x,u)= 0 x∈ RN N ≥ 3 where u →f(x,u) is not assumed to be regular near u = 0 and f(x,u) may be more general involving both singular and sublinear terms. Some sufficient conditions are given with the aid of the barrier method and ODE approach, which guarantee the existence of positive entire solutions that tend to any sufficiently large constants arbitrarily prescribed in advance.
文摘A class of singularly perturbed problems for the nonlinear elliptic equations is considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems are studied, which reduced equations possess two intersecting solutions.
文摘The singularly perturbed problems for the nonlinear elliptic systems in the half space are considered. Under suitable conditions, using the comparison theorem the existence and asymptotic behavior of solution for the boundary value problem are studied.
文摘The authors consider the existence of singular limit solutions for a family of nonlinear elliptic problems with exponentially dominated nonlinearity and Dirichlet boundary condition and generalize the results of [3].
