Semilinear nonlocal elliptic equations with critical and supercritical exponents

Abstract

we establish regularity results of solutions of above equation (whenever solution exists) and we show that every solution is a classical solution. Next, we derive certain decay estimate of solutions and the gradient of solutions at infinity for all Using those decay estimates, we prove Pohozaev type identity in RNRN and we show that the above problem does not have any solution when We also discuss radial symmetry and decreasing property of the solution and prove that when the above problem admits a solution. Moreover, if we consider the above equation in a bounded domain with Dirichlet boundary condition, we prove that it admits a solution for every and every solution is a classical solution.