Nonlinear Analysis-Real World Applications最新文献

In this paper we consider a non-linear Robin problem driven by the Orlicz $g$-Laplacian operator. Using variational technique combined with a suitable truncation and Morse theory (critical groups), we prove two multiplicity theorems with sign information for all the solutions. In the first theorem, we establish the existence of at least two non-trivial solutions with fixed sign. In the second, we prove the existence of at least three non-trivial solutions with sign information (one positive, one negative, and the other change sign) and order. The result of the nodal solution is new for the non-linear $g$-Laplacian problems with the Robin boundary condition.

The existence of backward bifurcation indicates an obstacle to disease eradication even when the basic reproduction number falls below unity. Bifurcation analysis allows us to identify causes for backward bifurcation, thereby helping to design a strategy to avoid such phenomena for disease eradication. In this study, we perform an in-depth bifurcation analysis of a malaria model incorporating cross-border mobility between two countries to explore mobility’s role in backward bifurcation. Our analysis reveals that cross-border mobility can be a primary driving force for backward bifurcation in malaria dynamics. This novel result with cross-border mobility bringing backward bifurcation advances the traditional idea of disease-induced death being the primary driver of backward bifurcation. Using the malaria case in Nepal with cross-border mobility between Nepal–India, we validated analytical results by numerical simulations. Our model predicts that the disease-free equilibrium exists only if cross-border mobility or infection abroad are absent and malaria eradication is possible in Nepal. Otherwise, there is the coexistence of three endemic equilibria with a lower and higher stable epidemic level. Results on the bifurcation of our model may be helpful to control dynamics in order to maintain the malaria epidemic at a low level if it cannot be eradicated due to the entry of cases through cross-border mobility.

This work is concerned with a competition system with nonlinear coupled reaction terms. By using Schauder’s fixed point theorem, we first prove the existence of a traveling wave solution connecting two uniform stationary states that do not satisfy the competitive ordering. Then some asymptotic spreading properties of the two species are obtained, and on this basis, we derive the multiplicity of asymptotic spreading speed of the considered system. Finally, numerical simulations corroborate the existence of traveling wave solutions satisfying different asymptotic conditions, which are theoretically established by the current paper and the reference.

We study a two-stage structured population model for which the juveniles diffuse purely by random walk while the adults exhibit long range dispersal. Questions on the persistence or extinction of the species are examined. It is shown that the population eventually dies out if the principal spectrum point ${\lambda }_p$ of the linearized system at the trivial solution is nonpositive. However, the species persists if ${\lambda }_p>0$. Moreover, at least one positive steady state exists when ${\lambda }_p>0$. The uniqueness and global stability of the positive steady-state solution is obtained under some special cases. We also establish a sup/inf characterization of ${\lambda }_p$.

This paper focuses on the existence and nonexistence of a time periodic traveling wave solution of a time-periodic reaction–diffusion SEIR epidemic model. The main feature of the model is the possible deficiency of the classical comparison principle such that many known results do not directly work. If the basic reproduction number of the model, denoted by $R_0$, is larger than one, there exists a minimal wave speed $c^{\ast }>0$ satisfying for each $c>c^{\ast }$, the system admits a nontrivial time periodic traveling wave solution with wave speed $c$ and for $c<c^{\ast }$, there exists no nontrivial time periodic traveling waves such that the system; if $R_0<1$, the system admits no nontrivial time periodic traveling waves.

In this article, we study the long-time asymptotic properties of a non-linear and non-local equation of diffusive type which describes the rock–paper–scissors game in an interconnected population. We fully characterize the self-similar solution and then prove that the solution of the initial–boundary value problem converges to the self-similar profile with an algebraic rate.

In this paper, we study the existence of solutions for the following eigenvalue problem: $\left(\mathrm{LP}\right)\left(\begin{array}{ccc}(-\Delta +d_1)(-\Delta +d_2)u+m\left(x\right)u=\lambda a\left(x\right)u& & \text{in}\Omega \\ u⁄\equiv 0,u\ge 0& & \text{in}\Omega \\ \Delta u=u=0& & \text{on}\partial \Omega \end{array}\right)$ where $\Omega \subset R^N$ is a smooth bounded domain, $d_1,d_2\in R$ and $a\left(\cdot \right),m\left(\cdot \right)\in L^{\infty }\left(\Omega \right)$ may have indefinite sign.

This paper deals with a PDE model of two species competing for a single limiting nutrient resource in the unstirred chemostat in which one microbial species is of the variable yield. The introduction of the variable yield makes the conservation law fail. We first investigate the uniqueness of positive steady-state solution and dynamical behavior of the single species model. Then we establish the existence and structure of coexistence solutions of two species system. It turns out that the positive bifurcation branch connects two semi-trivial solution branch. Finally, we analyze the dynamical behavior of two species system, and the result shows that the two species system is uniformly persistent.

In this paper, we study the orbital stability of traveling wave solutions to the Gallay and Mascia (GM) reduction of the Gatenby–Gawlinski model. The heteroclinic solutions provided by Gallay and Mascia represent the propagation of a tumor front into healthy tissue. Orbital stability is crucial to investigating models as it determines which solutions are likely to be observed in practice. Through constructing the unstable manifold to connect fixed states of the GM model and applying a shooting argument, we constructed front solutions. After numerically generating front solutions, we studied stability by constructing the spectrum for various parameters of the GM model. We see no evidence of point eigenvalues in the right half-plane, leaving the essential spectrum as the only possible source of instability. These findings show that Gallay and Mascia’s derived heteroclinic solutions are likely to be observed physically in biological systems and are stable for various tumor growth speeds.