Mountain Pass Theorem (MPT) is an important result in variational methods with multiple applications in partial differential equations involved in mathematical physics. Starting from a variant of MPT, a new result concerning the existence of the solution for certain mathematical physics problems involving p-Laplacian and p-pseudo-Laplacian has been obtained. Based on the main theorem, the existence, possibly the uniqueness, and characterization of solutions for models such as nonlinear elastic membrane, glacier sliding, and pseudo torsion problem have been obtained. The novelty of the work consists of the formulation of the central result under weaker conditions requested by the chosen variant of MPT, the proof of this statement, and its application in solving above mentioned problems. While the expressions of such Dirichlet and/or von Neumann problems were already completed, this proposed solving method suggests some specific numerical methods to construct the appropriate solution. A general goal of this paper is the extension of the applicative pallet of this way to construct the solutions encountered in modeling real processes developed within new emerging technologies.

This paper is aimed at providing three versions to solve and characterize weak solutions for Dirichlet problems involving thep-Laplacian and thep-pseudo-Laplacian. In this way generalized versions for some results which use Ekeland variational principle, critical points for nondifferentiable functionals, and Ghoussoub-Maurey linear principle have been proposed. Three sequences of generalized statements have been developed starting from the most abstract assertions until their applications in characterizing weak solutions for some mathematical physics problems involving the abovementioned operators.

Improving soil quality is of growing interest and, among optimal solutions, the reuse and recycling of biopolymers of pelt waste from the tannery industry have been proposed, one of them being for collagen hydrolysate with micronutrients and polymers incorporated, to be used as fertilizers for poor soils rehabilitation. As functionalization agents, polyacrylamide, starch and dolomite were included into biopolymer matrixes in order to enhance their specific efficiency. These fertilizers were adequately characterized for their physical–chemical properties, including nutrient content, and tested on three poor soils, while a fourth sample of normal soil was chosen for comparative purposes. These soils were also characterized for their texture and physical–chemical properties in order to establish the fertility state of the soils as a function of nutrient content. In this respect, a series of agrochemical tests were developed at laboratory scale, simulating real agriculture environments in a vegetation room, where a significant plant growth in height was observed for all the agro-hydrogels with nutrients encapsulated, and multiplication of the nodosities number was observed in the case of the soybean culture. The most significant effect was obtained in the case of the fertilizer functionalized with starch. Finally, the application dose of the organic fertilizers for specific culture plants was estimated, such as field cultures (cereals, corn), field vegetables, vineyards or fruit-growing plantations. These agro-collagen fertilizers are particularly recommended for amendment of field cereals and vegetables. The novelty of this study mainly consists of the recovery and recycling of the pelt waste as efficient fertilizers after their adequate functionalization with synthetic or natural biopolymers.

This paper brings together methods to solve and/or characterize solutions of some problems of mathematical physics equations involving p-Laplacian and p-pseudo-Laplacian. Using surjectivity or variational approaches, one may obtain or characterize weak solutions for Dirichlet or Newmann problems for these important operators. This article details three ways to use surjectivity results for a special type of operator involving the duality mapping and a Nemytskii operator, three methods starting from Ekeland’s variational principle and, lastly, one with a generalized variational principle to solve or describe the above-mentioned solutions. The relevance of these operators and the possibility of their involvement in the modeling of an important class of real phenomena determined the author to group these seven procedures together, presented in detail, followed by many applications, accompanied by a general overview of specialty domains. The use of certain variational methods facilitates the complete solution of the problem via appropriate numerical methods and computational algorithms. The exposure of the sequence of theoretical results, together with their demonstration in as much detail as possible has been fulfilled as an opportunity for the complete development of these topics.

This paper presents some variants of minimal point theorem together with corresponding variants of Ekeland variational principle. In the second part of this article, there is a discussion on Ekeland variational principle and minimal point theorem relative to it in uniform spaces. The aim of these series of important results is to highlight relations between them, some improvements and specific applications.

This paper aims to systematize a series of statistical methods of analysis and control and proposes some forecast models for surface water pollution both in and near a large city. The monitoring data of heavy metals, nitrites, and phosphates collected for three years are processed using different statistical tools. It is demonstrated that they are under statistical control, and appropriate mathematical models are formulated to allow for forecasting and understanding of the causes of the appearance and perpetuation of certain phenomena. A comparative analysis is made, and the generalization of some methods is considered as an analysis and control tool.