The aim of this paper is to explore the method lower and upper solutions in order give some existence results for equations form $$y^{(4)}(x)+(k_{1}+k_{2}) y''(x)+k_{1}k_{2} y(x)=f\bigl(x,y(x)\bigr), \quad x\in(0,1), $$ with Navier condition $$y(0) = y(1) y''(0) y''(1) 0 under $k_{1}<0<k_{2}<\pi^{2}$ . main tool Schauder fixed point theorem.

In this paper, we investigate the existence of an S-shaped component in solution set following fourth-order boundary value problem: $$\begin{aligned} \left \{ \textstyle\begin{array}{l} u''''(x)=\lambda f(x,u(x),u''(x)), \quad x\in (0,1), \\ u(0)=u(1)=u''(0)=u''(1)=0, \end{array}\displaystyle \right . \end{aligned}$$ where $f\in C( [0,1]\times [0,\infty )\times (-\infty,0], [0,\infty))$ , and $\lambda >0$ is a parameter. By figuring shape unbounded continua solutions, show multiplicity...

This paper deals with the existence of triple positive solutions for a type second-order singular boundary problems general differential operators. By using Leggett-Williams fixed point theorem, we establish an criterion at least three suitable growth conditions imposed on nonlinear term.

In this paper, we consider the existence and iterative approximation of solutions for a class nonlinear fourth-order integro-differential equations (IDEs) with Navier boundary conditions. We first prove uniqueness analytical linear IDE, which has rich applications in engineering physics, then establish maximum principle corresponding operator. Based upon principle, develop monotone technique presence lower upper to obtain nonlocal problem under certain Some examples are presented illustrate...

In this paper, we consider the solvability of a class nonlinear fourth order integro-differential equations with Navier boundary condition. We first deal corresponding linear problem and establish maximum principle. Using principle, develop monotone iterative technique in presence lower upper solutions to solve under certain conditions. Some examples are presented illustrate main results.

This paper is concerned with the existence and uniqueness of positive solutions for fourth order Kirchhoff type problemx ∈ (0, 1),where a > 0, b ≥ 0 are constants, λ R parameter.For case f (u) ≡ u, we use an argument based on linear eigenvalue problems equations their properties to show that there exists unique solution all 1,a , here first above problem = 0; sublinear, prove no < by using bifurcation method.

Named Entity Recognition (NER) is a pivotal challenge in the field of natural language processing. In medical field, NER plays crucial role identifying entities, such as diagnoses and drugs, from electronic records. To address issue incomplete inaccurate word recognition Chinese records, we propose BERT-BiLSTM-CRF model that incorporates both lexicon self-attention mechanism.In our approach, first utilize BERT for preprocessing to generate vectors. These vectors capture important semantic...

This paper is concerned with the existence of positive solutions for fourth order Kirchhoff type problem $$ \left\{\begin{array}{ll} \Delta^{2}u-(a+b\int_\Omega \nabla u ^2dx)\triangle u=\lambda f(u(x)),\ \ \text{in}\ \Omega,\\ u=\triangle u=0,\ \text{on}\ \partial\Omega,\\ \end{array} \right. where $\Omega\subset \mathbb{R}^{N}$($N\geq 1$) a bounded domain smooth boundary $\partial \Omega$, $a>0, b\geq 0$ are constants, $\lambda\in \mathbb{R}$ parameter. For case $f(u)\equiv u$, we use an...

We investigate the existence of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:math>-shaped connected component in set positive solutions fourth-order boundary value problem: id="M2"><mml:msup><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">′</mml:mi><mml:mi mathvariant="normal">′</mml:mi></mml:mrow></mml:msup><mml:mfenced...

This paper presents a new architecture of punctured Viterbi decoder with high-speed and low-power based on the modified T-algorithm trace-back method. To gain high throughput short decoding latency, parallel computations in ACSU SMU are adopted. Furthermore, to save power consumption, unnecessary path metric omitted add-compare-select-unit (ACSU) already generated back-tracing routes reused reduce times operations survivor-memory-unit (SMU). The latency (2,1,7) is only 34 clock cycles, total...

In this paper, we investigate the existence of a reversed S-shaped component in positive solutions set fourth-order boundary value problem $$\textstyle\begin{cases} u''''(x)=\lambda h(x)f(u(x)),\quad x\in(0,1),\\ u(0)=u(1)=u''(0)=u''(1)=0, \end{cases} $$ where $\lambda>0$ is parameter, $h\in C[0,1]$ and $f\in C[0,\infty )$ , $f(0)=0$ $f(s)>0$ for all $s>0$ . By figuring shape unbounded continua solutions, show multiplicity with respect to parameter λ, especially, obtain three distinct λ...

In this paper we study the existence of positive solutions for a class nonlocal fourth-order nonautonomous differential equations which can be seen as generalization extended Fisher-Kolmogorov and Swift-Hohenberg equations. The main result is proved using bifurcation theory.

In this paper, we study the existence of positive steady states for a nonlocal reaction‐diffusion model which describes growth single phytoplankton species with crowding effect caused by chemosensory aggregation in water column. Our result shows that under some conditions, is effective to populations. Based on key boundedness Lemma, main proved fixed point index theory and analytical techniques.

Chaos is a very complex phenomenon in deterministic nonlinear systems. In the development of just few decades, concept chaos has been extended to fields natural and social sciences. With deepening research, people begin study how simply control chaos. The theory chaotic synchronization makes realize that system dynamic characteristics can be applied practice. this work, we focus on transmission multiple memristor systems via single input method. First, based presented show internal behavior....