We deal with solutions vanishing at infinity in the class of the finite Dirichlet integral.
Scout bees deal with solutions which have been stopped updating, which avoids local optimum at some degree.
In this paper, we deal with solutions of problems (1.3) and (1.4) with finite Morse indices, which are possibly sign-changing.
However, the theorems in [19, 20] deal with solutions of the linear equation under some regularity conditions, for example, the continuity, convexity, differentiability, analyticity and so on, while Theorem 2.1 deals with the general solution of (1.7) without regularity conditions.
It will be focused on two different disciplines and related numerical approaches which deal with solutions of the mentioned task: form finding of prestressed membranes and general shape optimization.
Most of the previous studies dealt with solutions using Legendre, Chebyshev, and Gegenbauer polynomials.
One of the first works dealing with solutions concentrating around a sphere is [6] in which Ambrosetti, Malchiodi and Ni give necessary and sufficient conditions under which (1.1) exhibits solutions concentrating around a sphere.
A smaller number dealt with solutions.
The benefit of using evolutionary algorithms is in the ability to deal with complex solution spaces.
Also, there are many articles which deal with the solution and analysis of two-dimensional Fredholm and Volterra integral equations.
