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We study the behavior near the boundary conical point of weak solutions to the Dirichlet problem for elliptic quasi-linear second-order equation with the p -Laplacian and the strong nonlinearity on the right side.

We study the behavior near the boundary conical point of weak solutions to the Dirichlet and Robin problems for elliptic quasi-linear second-order equation with the p-Laplacian and the strong nonlinearity in the right side, as well as we consider the Dirichlet problem for p(x)-harmonic functions. We establish the exact estimate of the solutions modulus for our problems near a conical boundary point of the type \(|u(x)|=O(|x|^{\varkappa })\).