Abstract:
Let D be a bounded domain in ℝn(n≥2). We consider the following nonlinear elliptic problem: Δu=f(⋅,u) in D (in the sense of distributions), u|∂D=ϕ, where ϕ is a nonnegativecontinuous function on ∂D and f is a nonnegativefunction satisfying some appropriate conditions related to someKato class of functions K(D). Our aim is to prove that the aboveproblem has a continuous positive solution bounded below by afixed harmonic function, which is continuous on D¯. Next, we will be interested in the Dirichlet problem Δu=−ρ(⋅,u) in D (in the sense of distributions), u|∂D=0, where ρ is a nonnegative function satisfying some assumptions detailed below.Our approach is based on the Schauder fixed-point theorem.

Abstract:
This paper is concerned with the existence of bounded positive solution for the semilinear elliptic problem in subject to some Dirichlet conditions, where is a regular domain in ？ with compact boundary. The nonlinearity is nonnegative continuous and the potential belongs to some Kato class . So we prove the existence of a positive continuous solution depending on by the use of a potential theory approach. 1. Introduction In this paper, we study the existence of positive bounded solution of semilinear elliptic problem where is a -domain in with compact boundary, and are fixed nonnegative constants such that , and when is bounded. The parameter is nonnegative, and the function is nontrivial nonnegative and continuous on . Numerous works treated semilinear elliptic equations of the type For the case of nonpositive function , many results of existence of positive solutions are established in smooth domains or in , for instance, see [1–5] and the references therein. In the case where changes sign, many works can be cited, namely, the work of Glover and McKenna [6], whose used techniques of probabilistic potential theory for solving semilinear elliptic and parabolic differential equations in . Ma and Song [7] adapted the same techniques of those of Glover and McKenna to elliptic equations in bounded domains. More precisely, the hypotheses in [6, 7] require in particular that and on each compact, there is a positive constant such that . In [8], Chen et al. used an implicit probabilistic representation together with Schauder's fixed point theorem to obtain positive solutions of the problem ( ). In fact, the authors considered a Lipschitz domain in , with compact boundary and imposed to the function to satisfy on , where is nonnegative Borel measurable function defined on and the potentials are nonnegative Green-tight functions in . In particular, the authors showed the existence of solutions of ( ) bounded below by a positive harmonic function. In [9], Athreya studied ( ) with the singular nonlinearity , , in a simply connected bounded -domain in . He showed the existence of solutions bounded below by a given positive harmonic function , under the boundary condition , where is a constant depending on , , and . Recently, Hirata [20] gave a Chen-Williams-Zhao type theorem for more general regular domains . More precisely, the author imposed to the function to satisfy where the potential belongs to a class of functions containing Green-tight ones. We remark that the class of functions introduced by Hirata coincides with the classical Kato class introduced for

Abstract:
Let D be a bounded domain in n ( n ≥ 2 ) . We consider the following nonlinear elliptic problem: Δ u = f ( , u ) in D (in the sense of distributions), u | D = , where is a nonnegative continuous function on D and f is a nonnegative function satisfying some appropriate conditions related to some Kato class of functions K ( D ) . Our aim is to prove that the above problem has a continuous positive solution bounded below by a fixed harmonic function, which is continuous on D ˉ . Next, we will be interested in the Dirichlet problem Δ u = ρ ( , u ) in D (in the sense of distributions), u | D = 0 , where ρ is a nonnegative function satisfying some assumptions detailed below. Our approach is based on the Schauder fixed-point theorem.

Abstract:
Let $D$ be an unbounded domain in $mathbb{R}^{n}$ ($ngeq 2$) with a nonempty compact boundary $partial D$. We consider the following nonlinear elliptic problem, in the sense of distributions, $$displaylines{ Delta u=f(.,u),quad u>0quad hbox{in }D,cr uig|_{partial D}=alpha varphi ,cr lim_{|x|o +infty }frac{u(x)}{h(x)}=eta lambda , }$$ where $alpha ,eta,lambda $ are nonnegative constants with $alpha +eta >0$ and $varphi $ is a nontrivial nonnegative continuous function on $partial D$. The function $f$ is nonnegative and satisfies some appropriate conditions related to a Kato class of functions, and $h$ is a fixed harmonic function in $D$, continuous on $overline{D}$. Our aim is to prove the existence of positive continuous solutions bounded below by a harmonic function. For this aim we use the Schauder fixed-point argument and a potential theory approach.

Abstract:
We study the semilinear elliptic system $$ Delta u=lambda p(x)f(v),Delta v=lambda q(x)g(u), $$ in an unbounded domain D in $ mathbb{R}^2$ with compact boundary subject to some Dirichlet conditions. We give existence results according to the monotonicity of the nonnegative continuous functions f and g. The potentials p and q are nonnegative and required to satisfy some hypotheses related on a Kato class.

Abstract:
We present existence results for the polyharmonic nonlinear elliptic boundary-value problem $$displaylines{ (-Delta )^m u=f(cdot,u) quad hbox{in }B cr (frac{partial }{partial u })^j u=0quad hbox{on }partial B, quad 0leq jleq m-1. }$$ (in the sense of distributions), where $B$ is the unit ball in $mathbb{R}^n$ and $ngeq 2$. The nonlinearity $f(x,t)$ satisfies appropriate conditions related to a Kato class of functions $K_{m,n}$. Our approach is based on estimates for the polyharmonic Green function with zero Dirichlet boundary conditions and on the Schauder fixed point theorem.

Abstract:
The global awareness regarding economy expansion and
environmental preservation in the same time made the solar energy investment a
vivid topic nowadays more than before. The solar energy project or the new
Saudi oil made by the crown prince Mohammad bin SalmanAl Saud was the focus of the current study. We
designed the questionnaire with three categories to assess citizens of Saudi Arabia awareness
about solar energy represented by photovoltaic system. The responses collected
electronically from 424 respondents ranged between 18 - 41years old
to examine their awareness and acceptance of the solar system. The results
showed a positive tendency of solar panel installment and useinstead of electricity as
source of energy. The respondents’ confidence of photovoltaic use ability to
reduce electricity bills was positive. Moreover, the Saudi public awareness and
approval of electricity bills regulation were in agreement with the government policy. Around 30%
of respondents thought that solar energy is the sole source of energy where
they resident. While 75% of respondents thought, they might get greater benefit
from solar energy in comparison of the other renewable resources as wind and
earth energy. The study emphasized the great awareness of Saudi public views
analogues with the global trend and energy shift. The Photovoltaic (PV) system
will be the vital investment in Saudi Arabia near future with great approval of
public and government system.

Abstract:
Understanding the ecology of soil rhizosphere is essential to enhancing soil ecosystem and plants productivity. Poor-soil properties can limit rhizosphere microbial composition, interactions and plants productivity. Furthermore, the presence of plant exudates and microbial interation can change the rhizosphere dynamic. In the current study, we used two types of soils, rich nutrient soil represented by potting-soil and poor-soil represented with nutrient-deprived poor-soil. The two types of soil were inoculated with five microbial combinations using plant growth promoting bacteria (PGPB, Pseudomonas fluorescens) and mycorrhiza, and planted with two-day-old sorghum bicolor and Setaria italica (Foxtail millet) seedlings. Soil elements analyses were conducted 60 days after planting. The availability of exchangeable base alkali elements (Ca, Mg, Na) were measured and compared. Na was exclusively affected by PGPB inoculation in both soil types. Ca and Mg increased highest when associated with arbuscular inoculation, exclusively, in comparison to association with PGPB or Ectomycorrhiza in both soil types when planted with sorghum. Whereas, the same elements Ca and Mg, increased highest when associated with arbuscular mycorrhiza inoculation whether combined with PGPB or ectomycorrhiza when in soil planted with Setaria italica. The mycorrhiza increased Ca and Mg availability when combined with PGPB. Naincrease was associated only with PGPB inoculation solely in both soil types. The use of arbuscular mycorrhiza inoculation combined with PGPB is ecofriendly method to enrich rhizosphere in poor-soil and eliminate the need to use any chemical fertilizers.

Abstract:
The role of universities is centered on education and qualification to raise the level of science and awareness in society. Considering the global economic changes, it is necessary to prepare universities to raise their level of physical in parallel with raising the academic and research level. In the current research, we conducted an electronic questionnaire targeting a random group of young men and women, the majority of whom were in the age group 20 to 35 years old. Responses ranged from strong approval to support and even total rejection of the use of paid services provided by the university, but the vast majority approved strongly. It was also found that most of the random sample concerned by the quality of the services provided by the university from workshops, courses and exhibitions to serve the rehabilitation of the labor. In addition, documentation of the attendance with a certificate was highly demanded. The results also indicated a general acceptance to pay 5% of the value of the profits of sales in case of presentation at the university and the nomination of the best price for the short courses of the university ranged from 100 - 200 Saudi Riyals (SAR). Therefore, the study shows a general acceptance of the concept of paid services because of the system of the free educational systems in Saudi Arabia, which makes the availability of short courses and workshops at an acceptable price is welcomed. Strengthening the financial resources of Saudi universities is a challenge that can be overcome while ensuring community cooperation and greater transparency. The means of strengthening financial resources can be limited using two methods. First, provide a variety of services at competitive prices. Second, reduce financial waste resulting from energy misuse of learning resources, such as chemicals, operating plants and devices, by linking the different faculties at the university to a single database. The data base will ensure to enable users of academics, researchers and graduate students to screen resources availability and avoid duplication of requests in case of adequate coverage.