Concentration estimates for Emden-Fowler equations with boundary singularities and critical growth

Concentration estimates for Emden-Fowler equations with boundary singularities and critical growth

We establish –among other things– existence and multiplicity of solutions for the Dirichlet problem ∑ i ∂iiu+ |u| ⋆−2 u |x|s = 0 on smooth bounded domains Ω of R (n ≥ 3) involving the critical Hardy-Sobolev exponent 2 = 2(n−s) n−2 where 0 < s < 2, and in the case where zero (the point of singularity) is on the boundary ∂Ω. Just as in the Yamabe-type non-singular framework (i.e., when s = 0), th...

Quasi-Lie schemes and Emden–Fowler equations

The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalisations is given. As a first result we obtain t-dependent constants of the motion for particular instances of Emden equations by means of some of their particular solutions. Previously known results are recovered from t...

Symmetry and nonexistence results for Emden-Fowler equations in cones

Approximate solutions of Emden-Fowler type equations

Singular initial value problems are investigated. We extend a decomposition method for di¤erent type Emden-Fowler-like equations. Some special cases of the equation are solved as examples, to illustrate the reliableness of the method. The solutions are constructed in the form of a convergent series.

Numerical Solution of the Time Dependent Emden- Fowler Equations with Boundary Conditions using Modified Decomposition Method

We propose a new modification to Adomian decomposition method for numerical treatment of the time-dependent EmdenFowler-types equations with the Neumann and Dirichlet boundary conditions. In new modified method, we use all the boundary conditions to derive an integral equation before establishing the recursive scheme. The new modified decomposition method (MDM) will be used without unknown cons...