Abstract:
This paper is concerned with the investigation of solutions with a point singularity of the general elliptic equation
$$
-\sum_{i=1}^n\frac\partial{\partial x_i}
\biggl(\biggl|\frac{\partial u}{\partial x_i}\biggr|^{p_i-2}\frac{\partial u}{\partial x_i}\biggr)+|u|^{q-1}u=0.
$$
A method for deriving new pointwise estimates for the solution and integral estimates for the gradient of the solution is developed. Precise conditions are established on the behaviour of the term characterizing the absorption to ensure the non-existence of solutions with a point singularity.
Bibliography: 11 titles.
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