Solutions to semilinear p-Laplacian Dirichlet problem in population dynamics

Abstract

In this article, we study a semilinear p-Laplacian Dirichlet problem arising in population dynamics. We obtain the Morse critical groups at zero. The results show that the energy functional of the problem is trivial. As a consequence, the existence and bifurcation of the nontrivial solutions to the problem are established.

Approximation in Smirnov classes with variable exponent

“…Nowadays, there are sufficiently wide investigations relating to the fundamental problems of these spaces, in view of potential theory, maximal and singular integral operator theory and others. The sufficiently wide presentation of the corresponding results can be found in the monographs [1][2][3] and also in the papers, [4][5][6][7][8][9][10] relating to the results obtained in the complex plane. But the approximation problems in the variable exponent Lebesgue spaces, especially in the complex plane are not investigated sufficiently wide.…”