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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Global Bifurcation Of Positive Solutions For A Class Of Superlinear First-Order Differential Systems, Lijuan Yang, Ruyun Ma
Global Bifurcation Of Positive Solutions For A Class Of Superlinear First-Order Differential Systems, Lijuan Yang, Ruyun Ma
Turkish Journal of Mathematics
We are concerned with the first-order differential system of the form $$\left\{ \begin{array}{ll} u'(t)+a(t)u(t)=\lambda b(t) f(v(t-\tau(t))), &t\in\mathbb{R},\\ v'(t)+a(t)v(t)=\lambda b(t)g(u(t-\tau(t))), &t\in\mathbb{R},\\ \end{array} \right. $$ where $\lambda\in\mathbb{R}$~is a parameter. $a,b\in C(\mathbb{R},[0,+\infty))$ are two $\omega$-periodic functions such that $\int_0^\omega a(t)\text{d}t>0$,~$\int_0^\omega b(t)\text{d}t>0$,~$\tau\in C(\mathbb{R},\mathbb{R})$ is an $\omega$-periodic function. The nonlinearities~$f,g\in C(\mathbb{R},(0,+\infty))$~are two nondecreasing continuous functions and satisfy superlinear conditions at infinity.~By using the bifurcation theory,~we will show the existence of an unbounded component of positive solutions, which is bounded in positive $\lambda$-direction.
Existence And Multiplicity For Positive Solutions Of A System Of First Order Differential Equations With Multipoint And Integral Boundary Conditions, Le Thi Phuong Ngoc, Nguyen Thanh Long
Existence And Multiplicity For Positive Solutions Of A System Of First Order Differential Equations With Multipoint And Integral Boundary Conditions, Le Thi Phuong Ngoc, Nguyen Thanh Long
Turkish Journal of Mathematics
In this paper, we state and prove theorems related to the existence and multiplicity for positive solutions of a system of first order differential equations with multipoint and integral boundary conditions. The main tool is the fixed point theory. In order to illustrate the main results, we present some examples.
Existence Of Positive Solutions For Nonlinear Multipoint P-Laplacian Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Existence Of Positive Solutions For Nonlinear Multipoint P-Laplacian Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
In this paper, we investigate the existence of positive solutions for nonlinear multipoint boundary value problems for p-Laplacian dynamic equations on time scales with the delta derivative of the nonlinear term. Sufficient assumptions are obtained for existence of at least twin or arbitrary even positive solutions to some boundary value problems. Our results are achieved by appealing to the fixed point theorems of Avery-Henderson. As an application, an example to demonstrate our results is given.
Entire Large Positive Radial Symmetry Solutions For Combined Quasilinear Elliptic System, Seshadev Padhi, Smita Pati
Entire Large Positive Radial Symmetry Solutions For Combined Quasilinear Elliptic System, Seshadev Padhi, Smita Pati
Turkish Journal of Mathematics
We prove the existence of entire large positive solutions to the system \begin{equation*} \begin{cases} (r^{N-1}\phi_{1}(u^{\prime}))^{\prime} = r^{N-1}P_{1}(r)f(u,v),\, \, 0 \leq r < \infty \\ (r^{N-1}\phi_{2}(v^{\prime}))^{\prime} = r^{N-1}P_{2}(r)g(u,v),\, \, 0 \leq r < \infty \\ u(0) = a, \, v(0) = b, \, u^{\prime}(0) = 0, \, v^{\prime}(0) = b, \end{cases} \end{equation*} where the functions $\phi_{i}(s) = \alpha_{i}(s^{2})s, \,\, i= 1, 2$ are odd, increasing homeomorphisms, $P_{1},P_{2}:[0,\infty)\to [0,\infty)$ are continuous, and $f,g:[0,\infty) \times [0,\infty) \to [0,\infty)$ are continuous and increasing functions.
Solutions To Nonlinear Second-Order Three-Point Boundary Value Problems Of Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Solutions To Nonlinear Second-Order Three-Point Boundary Value Problems Of Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
In this paper, we consider existence criteria of three positive solutions of three-point boundary value problems for $p$-Laplacian dynamic equations on time scales. To show our main results, we apply the well-known Leggett-Williams fixed point theorem. Moreover, we present some results for the existence of single and multiple positive solutions for boundary value problems on time scales, by applying fixed point theorems in cones. The conditions we used in the paper are different from those in [Dogan A. On the existence of positive solutions for the one-dimensional $ p $-Laplacian boundary value problems on time scales. Dynam Syst Appl 2015; …
Positive Solutions Of First Order Boundary Value Problems With Nonlinear Nonlocal Boundary Conditions, Smita Pati, Seshadev Padhi
Positive Solutions Of First Order Boundary Value Problems With Nonlinear Nonlocal Boundary Conditions, Smita Pati, Seshadev Padhi
Turkish Journal of Mathematics
We consider the existence of positive solutions of the nonlinear first order problem with a nonlinear nonlocal boundary condition given by $x^{\prime}(t) = r(t)x(t) + \sum_{i=1}^{m} f_i(t,x(t)), t \in [0,1]$ $\lambda x(0) = x(1) + \sum_{j=1}^{n} \Lambda_j(\tau_j, x(\tau_j)),\tau_j \in [0,1],$ where $r:[0,1] \rightarrow [0,\infty)$ is continuous, the nonlocal points satisfy $0 \leq \tau_1 < \tau_2 < ... < \tau_n \leq 1$, the nonlinear functions $f_i$ and $\Lambda_j$ are continuous mappings from $[0,1] \times [0,\infty) \rightarrow [0,\infty)$ for $i = 1,2,...,m$ and $j = 1,2,...,n$ respectively, and $\lambda >1$ is a positive parameter. The Leray-Schauder theorem and Leggett--Williams fixed point theorem were used to prove our results.
Multiple Positive Solutions Of Nonlinear $M$-Point Dynamic Equations For $P$-Laplacian On Time Scales, Abdülkadi̇r Doğan
Multiple Positive Solutions Of Nonlinear $M$-Point Dynamic Equations For $P$-Laplacian On Time Scales, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
In this paper, we study the existence of positive solutions of a nonlinear $ m $-point $p$-Laplacian dynamic equation $$(\phi_p(x^\Delta(t)))^\nabla+w(t)f(t,x(t),x^\Delta(t))=0,\hspace{2cm} t_1< t 1.$ Sufficient conditions for the existence of at least three positive solutions of the problem are obtained by using a fixed point theorem. The interesting point is the nonlinear term $f$ is involved with the first order derivative explicitly. As an application, an example is given to illustrate the result.
Second-Order Nonlinear Three Point Boundary-Value Problems On Time Scales, S. Gülşan Topal
Second-Order Nonlinear Three Point Boundary-Value Problems On Time Scales, S. Gülşan Topal
Turkish Journal of Mathematics
We consider a second order three point boundary value problem for dynamic equations on time scales and establish criteria for the existence of at least two positive solutions of an eigenvalue problem by an application of a fixed point theorem in cones. Existence result for non-eigenvalue problem is also given by the monotone method.
On Positive Solutions Of Boundary Value Problems For Nonlinear Second Order Difference Equations, Nüket Aykut, Gusein Sh. Guseinov
On Positive Solutions Of Boundary Value Problems For Nonlinear Second Order Difference Equations, Nüket Aykut, Gusein Sh. Guseinov
Turkish Journal of Mathematics
In this paper we study nonlinear second order difference equations subject to separated linear boundary conditions. Sign properties of the associated Green's functions are investigated and existence results for positive solutions of the nonlinear boundary value problem are established. Upper and lower bounds for these positive solutions also are given.