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In this paper, we investigate the existence of homoclinic solutions for a class of fourth-order nonautonomous differential equations [ABSTRACT FROM AUTHOR]

The authors comment on a research paper on the use of the cystic fibrosis (CF) pig model to examine bacterial-dependent and -independent inflammatory responses and mucus accumulation in newborn pigs, which references a study by D.C. Bouzek et al., published within the issue. Topics discussed include the characterization of CF, overexpression of proinflammatory proteins in fetal lung tissue, and the effects on airway bacterial burden and airway inflammation.

In this paper, we study the existence of periodic solutions to the following prescribed mean curvature Liénard equation with a singularity and a deviating argument: where g has a strong singularity at $x=0$ and satisfies a small force condition at $x=\infty$. By applying Mawhin's continuation theorem, we prove that the given equation has at least one positive T-periodic solution. We will also give an example to illustrate the application of our main results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of a homoclinic solution is studied for the prescribed mean curvature Liénard equation $(\frac{u'(t)}{\sqrt{1+(u'(t))^{2}}})'+f(u(t))u'(t)+g(u(t))=p(t)$, where $f\in C(R,R)$, $g\in C^{1}(R,R)$, and $p\in C(R,R)$. Under some conditions, the author obtains the result that the equation has at least one nontrivial homoclinic solution for $p(t)\not\equiv0$, and the equation has no nontrivial homoclinic solution for $p(t)\equiv0$. The arguments are based upon Mawhin's continuation theorem. [ABSTRACT FROM AUTHOR]

We study the existence of periodic solutions for second-order neutral functional differential systems with operator varying in time and delays. An interesting issue is that the coefficient matrix of the neutral difference operator is not a constant matrix, which contradicts the available literature data. Some properties of the neutral difference operator variable as a function of time and the results on the existence of periodic solutions of the second-order neutral functional differential systems are obtained. Moreover, numerical simulations are performed to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a species predator-prey model given a reaction-diffusion system. It incorporates the Holling type II functional response and a quadratic intra-predator interaction term. We focus on the qualitative analysis, bifurcation mechanisms and pattern formation. We present the results of numerical experiments in two space dimensions and illustrate the impact of the diffusion on the Turing pattern formation. For this diffusion system, we also observe non-Turing structures such as spiral wave, target pattern and spatiotemporal chaos resulting from the time evolution of these structures. [ABSTRACT FROM AUTHOR]

This paper is concerned with a non-Newtonian filtration equation with nonlinear sources. By using an extension of Mawhin's continuation theorem and some analysis methods, we obtain some existence results of solitary wave and periodic wave solutions for the non-Newtonian filtration equation with nonlinear sources. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the authors investigate some new properties of nonlinear difference operator in the first, which is associated with neutral functional differential equations. Then, by using these new properties, the problem of existence of periodic solutions for neutral functional differential system with nonlinear operator is studied. The interesting thing is that the periodic solution to the system is allowed to be not differentiable. [Copyright &y& Elsevier]

Abstract: A new result for the existence of homoclinic orbits is obtained for ordinary p-Laplacian system , where p >1, t ∈ R, u ∈ R n and V ∈ C 1(R × R n , R), V(t, x)=−K(t, x)+ W(t, x) is T-periodic with respect to t, T >0 and f : R → R n is a continuous and bounded function. This result generalizes and improves some known results in the previous literature. [Copyright &y& Elsevier]

Abstract: A new result for the existence of homoclinic orbits is obtained for the second-order Hamiltonian system , where , , is -periodic with respect to , and is a continuous and bounded function. This result generalizes and improves some known results in the previous literature. [Copyright &y& Elsevier]

Abstract: A new result for existence of homoclinic orbits is obtained for the second-order Hamiltonian systems under a class of new superquadratic conditions. A homoclinic orbit is obtained as a limit of solutions of a certain sequence of boundary-value problems which are obtained by the minimax methods. [Copyright &y& Elsevier]

Abstract: In this paper, we study the existence of periodic solutions for a fourth-order -Laplacian differential equation with a deviating argument as follows: Under various assumptions, the existence of periodic solutions of the problem is obtained by applying Mawhin’s continuation theorem. [Copyright &y& Elsevier]

Abstract: By means of Mawhin’s continuation theorem, we study a class of p-Laplacian Duffing type differential equations of the form Some new results on the existence and uniqueness of periodic solutions for the above equation are obtained. It is significant that the growth degree with respect to the variables imposed on is allowed to be greater than , so our results generalize and improve on the corresponding results in related papers. [Copyright &y& Elsevier]