Exact Multiplicity of Sign-Changing Solutions for a Class of Second-Order Dirichlet Boundary Value Problem with Weight Function

Using bifurcation techniques and Sturm comparison theorem, we establish exact multiplicity results of sign-changing or constant sign solutions for the boundary value problems u″+a(t)f(u)=0, t∈(0, 1), u(0)=0, and u(1)=0, where f∈C(ℝ,ℝ) satisfies f(0)=0 and the limits f∞=lim|s|→∞(f(s)/s), f0=lim|s|→0(f(s)/s)∈{0,∞}. Weight function a(t)∈C1[0,1] satisfies a(t)>0 on [0,1]

Global Behavior of the Components for the Second Order m-Point Boundary Value Problems

We consider the nonlinear eigenvalue problems u″+rf(u)=0, 00 for i=1,…,m−2, with ∑i=1m−2αi<1; r∈â„Â; f∈C1(â„Â,â„Â). There exist two constants s2<0<s1 such that f(s1)=f(s2)=f(0)=0 and f0:=limu→0(f(u)/u)∈(0,∞), f∞:=lim|u|→∞(f(u)/u)∈(0,∞). Using the global bifurcation techniques, we study the global behavior of the components of nodal solutions of the above problems

Exact multiplicity of positive solutions for a p-Laplacian equation with positive convex nonlinearity

A p-Laplacian nonlinear elliptic equation with positive and p-superlinear nonlinearity and Dirichlet boundary condition is considered. We first prove the existence of two positive solutions when the spatial domain is symmetric or strictly convex by using a priori estimates and topological degree theory. For the ball domain in R-N with N \u3e= 4 and the case that 1 \u3c p \u3c 2, we prove that the equation has exactly two positive solutions when a parameter is less than a critical value. Bifurcation theory and linearization techniques are used in the proof of the second result. (C) 2015 Elsevier Inc. All rights reserved

Bearing Capacity of Large Drilled Shafts Fully Embeded in Claystone and Sandstone Layers

This paper focuses on analyzing the bearing capacity of large diameter drilled shafts that are fully embedded in the claystone and sandstone layers. The foundations used are the drilled shafts for the Pulau Balang bridge pylons built across the Balikpapan bay. Three bored pile foundations with a planned diameter of 2 meters by 60 meters were used. The bearing capacity of the foundation in the field was carried out using the Osterberg cell test. The bearing capacity of the upper side of the foundation is 32.77, 27.26, and 114.46 MN, and the lower parts are 26.98, 27.16, and 50.25 MN, respectively. The results show that the method closest to the upper part of the OC test is the method suggested by Kulhawy and Phoon, with a value of C = 0.5. As for the lower part, the closest approach is the combination of the Kulhawy and Phoon and the Rowe and Armitage methods. The combinations of methods that approximate&nbsp;the total bearing capacity of the field are the Kulhawy and Phoon (1993) and Rowe and Armitage (1987) methods for the dominant claystone layer, and the O'Neil and Reese (1993) and Rowe and Armitage (1987) methods for the main sandstone layer

Tinjauan Yuridis Perlindungan Hukum yang Dimiliki Oleh Content Creator Youtube yang Memperoleh Predikat Silver Play Button

This study aims to determine the legal protection of the YouTube Silver Play Button content creator for acts of plagiarism according to law number 28 of 2014. The Silver Play Button is a predicate that has been given by YouTube because it has succeeded in reaching 100,000 thousand subscribers. Therefore, this study explains the mechanism of copyright protection on Youtube, it can use Content ID and Web Forms and according to Law Number 28 of 2014 according to Article 113, and can be through APS as well as Arbitration. According to Islamic law, the sanctions imposed are in the form of ta'zir punishment, which means that it can be decided by the policy makers, namely the judge. The approach method used is normative. The data source is secondary data. The method used in analyzing this research is descriptive qualitative. The results of this study explain that Nanda Putri has committed plagiarism in the form of musical compositions referring to lyrics and music that can be written or recorded electronically and includes channel identity impersonation

Uniqueness of positive solutions for a class of elliptic systems

AbstractIn this article, we consider uniqueness of positive radial solutions to the elliptic system Δu+a(|x|)f(u,v)=0, Δv+b(|x|)g(u,v)=0, subject to the Dirichlet boundary condition on the open unit ball in RN (N⩾2). Our uniqueness results applies to, for instance, f(u,v)=uqvp, g(u,v)=upvq, p,q>0, p+q<1 or more general cases

Uniqueness of positive solutions of a class of ODE with nonlinear boundary conditions

We study the uniqueness of positive solutions of the boundary value problem u″+a(t)u′+f(u)=0, t∈(0,b), B1(u(0))−u′(0)=0, B2(u(b))+u′(b)=0, where 0<b<∞, B1 and B2∈C1(â„Â), a∈C[0,∞) with a≤0 on [0,∞) and f∈C[0,∞)∩C1(0,∞) satisfy suitable conditions. The proof of our main result is based upon the shooting method and the Sturm comparison theorem

Exact multiplicity of solutions for a class of two-point boundary value problems

We consider the exact multiplicity of nodal solutions of the boundary value problem $$displaylines{ u''+lambda f(u)=0 , quad tin (0, 1),cr u'(0)=0,quad u(1)=0, }$$ where $lambda in mathbb{R}$ is a positive parameter. $fin C^1(mathbb{R}, mathbb{R})$ satisfies $f'(u)>frac{f(u)}{u}$, if $u eq 0$. There exist heta_1<s_1<0<s_2<heta_2 such that $f(s_1)=f(0)=f(s_2)=0$; $uf(u)>0$, if u<s_1 or $u>s_2$; uf(u)<0, if s_1<u<s_2 and $u eq 0$; $int_{heta_1}^0 f(u)du=int_0^{heta_2} f(u)du=0$. The limit $f_infty=lim_{so infty} frac{f(s)}{s}in (0,infty)$. Using bifurcation techniques and the Sturm comparison theorem, we obtain curves of solutions which bifurcate from infinity at the eigenvalues of the corresponding linear problem, and obtain the exact multiplicity of solutions to the problem for $lambda$ lying in some interval in $mathbb{R}$

Global structure of positive solutions for superlinear 2m2mth-boundary value problems

summary:We consider boundary value problems for nonlinear $2m$th-order eigenvalue problem $$ \begin{aligned} (-1)^mu^{(2m)}(t)&=\lambda a(t)f(u(t)),\ \ \ \ \ 00$for some$t_0\in [0,1]$,$f\in C([0,\infty ),[0,\infty ))$and$f(s)>0$for$s>0$, and$f_0=\infty $, where$f_0=\lim _{s\rightarrow 0^+}f(s)/s$. We investigate the global structure of positive solutions by using Rabinowitz's global bifurcation theorem