Nodal solutions with synchronous sign changing components and Constant sign solutions for singular Gierer-Meinhardt type system
arXiv:2306.16742
Abstract
We establish the existence of three solutions for singular semilinear elliptic system, two of which are of opposite constant-sign. Under a strong singularity effect, the third solution is nodal with synchronous sign components. The approach combines sub-supersolutions method and Leray-Schauder topological degree involving perturbation argument.