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AFROUZI, G.A.,SHOKOOH, S.,CHUNG, N.T. The Korean Society for Computational and Applied M 2017 Journal of applied mathematics & informatics Vol.35 No.1
Using variational methods, we study the existence and multiplicity of weak solutions for some p(x)-Laplacian-like problems. First, without assuming any asymptotic condition neither at zero nor at infinity, we prove the existence of a non-zero solution for our problem. Next, we obtain the existence of two solutions, assuming only the classical Ambrosetti-Rabinowitz condition. Finally, we present a three solutions existence result under appropriate condition on the potential F.
AFROUZI, G.A.,ZAHMATKESH, H. The Korean Society for Computational and Applied M 2017 Journal of applied mathematics & informatics Vol.35 No.1
This study is concerned with the existence of positive solution for the following nonlinear elliptic system $$\{-M_1(\int_{\Omega}{\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^pdx)div({\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)\\{\hfill{120}}={\mid}x{\mid}^{-(a+1)p+c_1}\({\alpha}_1A_1(x)f(v)+{\beta}_1B_1(x)h(u)\),\;x{\in}{\Omega},\\-M_2(\int_{\Omega}{\mid}x{\mid}^{-bq}{\mid}{\nabla}v{\mid}^qdx)div({\mid}x{\mid}^{-bq}{\mid}{\nabla}v{\mid}^{q-2}{\nabla}v)\\{\hfill{120}}={\mid}x{\mid}^{-(b+1)q+c_2}\({\alpha}_2A_2(x)g(u)+{\beta}_2B_2(x)k(v)\),\;x{\in}{\Omega},\\{u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}$ is a bounded smooth domain of ${\mathbb{R}}^N$ with $0{\in}{\Omega}$, 1 < p, q < N, $0{\leq}a$ < $\frac{N-p}{p}$, $0{\leq}b$ < $\frac{N-q}{q}$ and ${\alpha}_i,{\beta}_i,c_i$ are positive parameters. Here $M_i,A_i,B_i,f,g,h,k$ are continuous functions and we discuss the existence of positive solution when they satisfy certain additional conditions. Our approach is based on the sub and super solutions method.
Afrouzi, Ghasem A.,Heidarkhani, Shapour,O'Regan, Donal Korean Mathematical Society 2010 대한수학회보 Vol.47 No.6
In this paper we establish the existence of at least three weak solutions for Neumann doubly eigenvalue elliptic systems driven by a ($p_1,\ldots,p_n$)-Laplacian. Our main tool is a recent three critical points theorem of B. Ricceri.
G.A. AFROUZI,H. ZAHMATKESH 한국전산응용수학회 2017 Journal of applied mathematics & informatics Vol.35 No.1
This study is concerned with the existence of positive solution for the following nonlinear elliptic system −M1 (∫ Ω |x|−ap|∇u|p dx ) div(|x|−ap|∇u|p−2∇u) = |x|−(a+1)p+c1 ( 1A1(x)f(v) + 1B1(x)h(u) ) ; x ∈ Ω; −M2 (∫ Ω |x|−bq|∇v|q dx ) div(|x|−bq|∇v|q−2∇v ) = |x|−(b+1)q+c2 ( 2A2(x)g(u) + 2B2(x)k(v) ) ; x ∈ Ω; u = v = 0; x ∈ @Ω; where Ω is a bounded smooth domain of RN with 0 ∈ Ω; 1 < p; q < N; 0 ≤ a < N−p p ; 0 ≤ b < N−q q and i; i; ci are positive parameters. Here Mi;Ai;Bi; f; g; h; k are continuous functions and we discuss the existence of positive solution when they satisfy certain additional conditions. Our approach is based on the sub and super solutions method
G.A. AFROUZI,S. SHOKOOH,N.T. CHUNG 한국전산응용수학회 2017 Journal of applied mathematics & informatics Vol.35 No.1
Using variational methods, we study the existence and multiplicity of weak solutions for some p(x)-Laplacian-like problems. First, without assuming any asymptotic condition neither at zero nor at infinity, we prove the existence of a non-zero solution for our problem. Next, we obtain the existence of two solutions, assuming only the classical Ambrosetti- Rabinowitz condition. Finally, we present a three solutions existence result under appropriate condition on the potential F.
Ghasem A. Afrouzi,Shapour Heidarkhani,Donal O'Regan 대한수학회 2010 대한수학회보 Vol.47 No.6
In this paper we establish the existence of at least three weak solutions for Neumann doubly eigenvalue elliptic systems driven by a (p1, … , pn)-Laplacian. Our main tool is a recent three critical points theorem of B. Ricceri.
Three solutions for a second-order Sturm-Liouville equation with impulsive effects
Hadi Haghshenas,Ghasem A. Afrouzi 한국전산응용수학회 2020 Journal of applied mathematics & informatics Vol.38 No.5
In this article, a second-order Sturm-Liouville problem with impulsive effects and involving the one-dimensional p-Laplacian is considered. The existence of at least three weak solutions via variational methods and critical point theory is obtained.
Abouzar Moshfegh,Ashkan Javadzadegan,Zhaoqi Zhang,Hamid Hassanzadeh Afrouzi,Mohammad Omidi 대한기계학회 2018 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.32 No.8
It is well accepted that blood flow in the human aorta is spiral by nature, with beneficial impacts for the cardiovascular system in the form of improved haemodynamics and efficient perfusion. This study investigates the effect of aortic spiral blood flow on wall shear stress (WSS) in computer-generated models of the left main trunk (LMT), also known as left main coronary artery, with varying take-off angle, stenosis severity and eccentricity. The results show that the spirality effect causes a substantial reduction in maximum WSS (WSS max ), average WSS (WSS ave ) and size of regions with low WSS. The effects of spiral flow on WSS max become more significant with increasing LMT take-off angle and stenosis eccentricity, and they become less significant with increasing stenosis severity. The aortic spiral blood flow intensity, LMT take-off angle, stenosis severity and eccentricity statistically significantly predict the WSS; however, the strongest predictor of WSS is stenosis severity (F(4, 399) = 3653.85, p < 0.001 for WSS max and F(4, 399) = 913.46, p < 0.001 for WSS ave ), followed by LMT take-off angle (F(4, 399) = 582.735, p < 0.001 for WSS max and F(4, 399) = 163.16, p < 0.001 for WSS ave ), stenosis eccentricity (F(4, 399) = 230.15, p < 0.001 for WSS max and F(4, 399) = 52.94, p < 0.001 for WSS ave ) and blood flow spirality (F(4, 399) = 112.37, p < 0.001 for WSS max and F(4, 399) = 32.18, p < 0.001 for WSS ave ). Our findings suggest that naturally or artificially induced spiral flow in the aorta potentially has atheroprotective effects in the LMT.