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This paper introduces a new concept of dual periodic boundary conditions. One of these conditions relates to the endpoints of an interval, while the other one involves two nonlocal positions within the interval. Under these boundary conditions, we establish the criteria for the existence of solutions for a fractional differential equation with p-Laplacian operator by using Mawhin's continuation theorem. An example is constructed for illustrating the obtained results. [ABSTRACT FROM AUTHOR]

This paper introduces a new concept of dual periodic boundary conditions. One of these conditions relates to the endpoints of an interval, while the other one involves two nonlocal positions within the interval. Under these boundary conditions, we establish the criteria for the existence of solutions for a fractional differential equation with p-Laplacian operator by using Mawhin's continuation theorem. An example is constructed for illustrating the obtained results.

In this paper, we study the existence, non-existence and uniqueness of periodic solutions for a class of higher order differential equations. The proof is based on the Mawhin’s continuation theorem and averaging method. Finally, two examples are given to illustrate the applicability of the conclusions of this paper. [ABSTRACT FROM AUTHOR]

Abstract The novelty of this paper is that, based on Mawhin’s continuation theorem, we present some sufficient conditions that ensure that there is at least one solution to a particular kind of a boundary value problem with the p-Laplacian and generalized fractional Caputo derivative.

Abstract In this paper, we study the existence and uniqueness of a periodic solution for a third-order neutral delay differential equation (NDDE) by applying Mawhin’s continuation theorem of coincidence degree and analysis techniques. An illustrative example is given as an application to support our results. To confirm the accuracy of our results, we also present a plot of the behavior of the periodic solution.

The novelty of this paper is that, based on Mawhin's continuation theorem, we present some sufficient conditions that ensure that there is at least one solution to a particular kind of a boundary value problem with the p-Laplacian and generalized fractional Caputo derivative. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of a periodic solution for a third-order neutral delay differential equation (NDDE) by applying Mawhin's continuation theorem of coincidence degree and analysis techniques. An illustrative example is given as an application to support our results. To confirm the accuracy of our results, we also present a plot of the behavior of the periodic solution. [ABSTRACT FROM AUTHOR]

We consider a Rayleigh-type equation with state–dependent delay ℘″(ϑ)+𝒱1(ϑ,℘(ϑ))+A(℘(ϑ−𝒱2(ϑ,℘(ϑ))))=B(ϑ).\wp ''\left( \vartheta \right) + \mathcal{V}{_1}\left( {\vartheta ,\wp \left( \vartheta \right)} \right) + A\left( {\wp \left( {\vartheta - \mathcal{V}{_2}\left( {\vartheta ,\wp \left( \vartheta \right)} \right)} \right)} \right) = B\left( \vartheta \right). We establish a set of new su˚cient conditions on the existence of at least one positive periodic solution by using the continuation theorem of coincidence degree theory. Our results not only provide a new approach but also generalize previous results. An example with graphical representations are presented to illustrate the results.

In this paper, by using the Mawhin's continuation theorem, some easily verifiable sufficient conditions are obtained to guarantee the existence of almost periodic solutions of impulsive non-autonomous Lotka-Volterra predator-prey system with harvesting terms. Our result corrects the result obtained in [13]. An example and some remarks are given to illustrate the advantage of this paper.

Abstract In this paper, the existence of positive periodic solutions is studied for super-linear neutral Liénard equation with a singularity of attractive type ( x ( t ) − c x ( t − σ ) ) ″ + f ( x ( t ) ) x ′ ( t ) − φ ( t ) x μ ( t ) + α ( t ) x γ ( t ) = e ( t ) , $$ \bigl(x(t)-cx(t-\sigma)\bigr)''+f\bigl(x(t) \bigr)x'(t)-\varphi(t)x^{\mu}(t)+ \frac{\alpha(t)}{x^{\gamma}(t)}=e(t), $$ where f : ( 0 , + ∞ ) → R $f:(0,+\infty)\rightarrow R$ , φ ( t ) > 0 $\varphi(t)>0$ and α ( t ) > 0 $\alpha(t)>0$ are continuous functions with T-periodicity in the t variable, c, γ are constants with | c | < 1 $|c| 1 $\mu>1$ by using Mawhin’s continuation theorem as well as the techniques of a priori estimates. At last, an example is given to show applications of the theorem.

Abstract By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with dim Ker L = 1 $\operatorname{dim}\operatorname{Ker}L = 1$ . And an example is given to show that our result here is valid.

In this article we study the existence and multiplicity of positive periodic solutions for two classes of non-autonomous fourth-order nonlinear ordinary differential equations $$\displaylines{ u^{iv}-pu'' -a(x)u^{n}+b(x)u^{n+2}=0, \cr u^{iv}-pu'' +a(x)u^{n}-b(x)u^{n+2}=0, }$$ where $n$ is a positive integer, $p \leq1$, and a(x),b(x) are continuous positive T-periodic functions. These equations include particular cases of the extended Fisher-Kolmogorov equations and the Swift-Hohenberg equations. By using Mawhin's continuation theorem, we obtain two multiplicity results these equations.

Abstract By constructing a suitable projection scheme and using the coincidence degree theory of Mawhin, we study the existence of solutions for conjugate boundary value problems with functional boundary conditions at resonance with dimKerL=1 $\operatorname{dim}\operatorname{Ker}L = 1$. Examples are given to illustrate our main results.

Abstract In this paper, by using Mawhin’s continuation theorem, we establish some sufficient conditions for the existence of at least one solution for a class of fractional infinite point boundary value problem at resonance. Moreover, an example is given to illustrate our results.

Abstract In this paper, by using Mawhin’s continuation theorem, we investigate the existence of solutions for a class of fractional differential equations with multi-point boundary value problems at resonance, and the dimension of the kernel for a fractional differential operator is three. An example is given to show our main result.

In this paper, we study the existence of positive periodic solutions for a class of non-autonomous second-order ordinary differential equations x ′ ′ + α x ′ + a (t) x n - b (t) x n + 1 + c (t) x n + 2 = 0 , where α ∈ R is a constant, n is a finite positive integer, and a(t), b(t), c(t) are continuous periodic functions. By using Mawhin's continuation theorem, we prove the existence and multiplicity of positive periodic solutions for these equations. [ABSTRACT FROM AUTHOR]

In this paper, by using an extension of Mawhin's continuation theorem and some analysis methods, we study the existence of periodic solutions for the following prescribed mean curvature system d d t φ (x ′) + ∇ W (x) = p (t) , where x ∊ ℝn, W ∊ C1(ℝn, ℝ), p ∊ C(ℝ, ℝn) is T-periodic and φ (x) x 1 + | x | 2 . [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the existence and global asymptotic stability of periodic solutions for a class of delayed discrete-time BAM neural networks. Instead of using the method of the priori estimate of periodic solutions in existing papers to study periodic solutions of neural networks, by combining Mawhin's continuation theorem of coincidence degree theory with linear matrix inequality (LMI) method as well as inequality techniques, some novel LMI-based sufficient conditions to guarantee the existence and global asymptotic stability of periodic solutions for the neural networks are established. Our results which are both dependent on time delay and external inputs of the neural networks are new and complementary to the existing papers. [ABSTRACT FROM AUTHOR]

By using some new analytical techniques, modified inequalities and Mawhin’s continuation theorem of coincidence degree theory, some sufficient conditions are obtained for the boundedness of the solution and the existence of at least one positive almost periodic solution of a kind of two-species model of facultative mutualism with time delays. Further, the global asymptotic stability of the positive almost periodic solution of this model is also considered. Some examples and numerical simulations are also given to illustrate the main results of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we study the singular fourth-order differential equation with a deviating argument: By using Mawhin's continuation theorem and some analytic techniques, we establish some criteria to guarantee the existence of positive periodic solutions. The significance of this paper is that g has a strong singularity at x = 0 and satisfies a small force condition at x = ∞, which is different from the known ones in the literature. [ABSTRACT FROM AUTHOR]

Abstract: This paper is devoted to investigating a class of complex‐valued neural networks with bounded and unbounded delays. By means of Mawhin's continuation theorem, some criteria on existence and uniqueness of periodic solution are established for the complex‐valued neural networks. By constructing an appropriate Lyapunov‐Krasovskii functional and M−matrix theory, some sufficient conditions are derived for the global exponential stability of periodic solutions to the complex‐valued neural networks. Finally, two numerical examples are given to show the effectiveness and merits of the present results. [ABSTRACT FROM AUTHOR]

In this paper, by using Mawhin's continuation theorem, we investigate the existence of solutions for a class of fractional differential equations with multi-point boundary value problems at resonance, and the dimension of the kernel for a fractional differential operator is three. An example is given to show our main result. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problems of existence and stability of the periodic solution for a class of neutral-type neural networks. The neural network addressed is general where the time delays and difference operator are taken into account. By employing the Mawhin's continuation theorem, the sufficient condition is obtained to guarantee the existence and uniqueness of the periodic solution for the neutral-type neural networks. By constructing a novel Lyapunov functional, a unified framework is established to derive sufficient conditions for the concerned system to be globally exponentially stable. A numerical example is provided to demonstrate the usefulness of the main results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of periodic solutions for fourth-order nonlinear differential equations. Under proper conditions, we employ a novel proof to establish some criteria to ensure the existence and uniqueness of $T$-periodic solutions. Moreover, we give two examples to illustrate the effectiveness of our main results.

By employing the continuation theorem of coincidence degree theory developed by Mawhin, we obtain periodic solution for a class of neutral differential equation with variable parameter and multiple deviating arguments.

In this paper, some sufficient conditions on the existence of $2k\pi$-periodic solutions for a kind of prescribed mean curvature Rayleigh equations are given. Then the existence of nontrivial homoclinic solutions for prescribed mean curvature Rayleigh equations is obtained. [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]

In this paper, a n-dimensional prescribed mean curvature Rayleigh p-Laplacian equation with a deviating argument, ... is studied. By means of Mawhin's continuation theorem and some analysis methods, a new result on the existence of homoclinic solutions for the equation is obtained. Our research enriches the contents of prescribed mean curvature equations. [ABSTRACT FROM AUTHOR]

In this paper, we analyze some properties of the linear difference operator A : CT → CT, [Ax](t) = x(t) - V(t)x(t-τ), and then, by using the coincidence degree theory of Mawhin, a kind of neutral differential systems with non-constant matrix is studied. Some new results on the existence of periodicity are obtained. It is worth noting that V(t) is no longer a constant matrix, which is different from the corresponding ones of past work. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with an existence result for periodic solutions for a class of fourth-order ordinary differential equations involving extended Fisher–Kolmogorov and Swift–Hohenberg equations, where, under a suitable growth condition on the nonlinear term, one proves an existence result by applying Mawhin’s continuation theorem. [Copyright &y& Elsevier]

In this paper, by using the Mawhin's continuation theorem, we obtain an existence theorem for some higher order multi-point boundary value problems at resonance in the following form: where $${f:[0,1]\times \mathbb{R}^n \to \mathbb{R}=(-\infty,+\infty)}$$ is a continuous function, $${e(t)\in L^1[0,1], p, k\in\{0,1,\ldots,n-1\}}$$ are fixed, m ≥ 3 for p ≤ k ( m ≥ 4 for p > k), $${\beta_j \in \mathbb{R}, j=1,2,\ldots,m-2, 0 < \eta_1 < \eta_2 < \cdots < \eta_{m-2} <1 }$$ . We give an example to demonstrate our results. [ABSTRACT FROM AUTHOR]

By means of Mawhin's continuation theorem and some analysis methods, the existence of 2 kT-periodic solutions is studied for a class of neutral functional differential equations, and then a homoclinic solution is obtained as a limit of a certain subsequence of the above periodic solutions set. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the authors first investigate some new properties of the -operator which is associated with neutral functional differential equations. Then, by using these new properties, the problem of existence of periodic solutions of the -operator neutral functional differential system is studied. The interesting thing is that the -operator is allowed to be unstable, which is generalized by the corresponding studies in the past under the crucial assumption that the -operator is stable. [Copyright &y& Elsevier]

Abstract: By means of Mawhin’s continuation theorem, the existence of periodic solution of the fourth-order -Laplacian differential equation with a deviating argument of the form is studied and some new results are obtained. [Copyright &y& Elsevier]

Abstract: Sufficient criteria are established for the existence of periodic solutions to a type of Duffing equation with state-dependent delay, which improve and generalize some related results in the literature. The approach is based on Mawhin’s continuation theorem. The significance of the present paper is that our results are relevant to delay by , which is different from the corresponding results of past work. [Copyright &y& Elsevier]

Abstract: Sufficient criteria are established for the existence of periodic solutions and three positive periodic solutions to a system with lossless transmission lines by using Mawhin’s continuation theorem and Leggett–Williams fixed point theorem. [Copyright &y& Elsevier]

Abstract: In this paper, by using inequality techniques and coincidence degree theory, some sufficient conditions are established for ensuring the existence of -periodic solutions for a class of fourth-order nonlinear differential equations. Two illustrative examples are provided to demonstrate that the results of this paper hold under weaker conditions than the existing ones, and are more effective. [Copyright &y& Elsevier]

Abstract: By means of Mawhin’s continuation theorem, a kind of p-Laplacian neutral functional differential equation with multiple variable parameters as follows: is studied. The interesting thing is that the coefficient is not a constant, by analyzing some properties of operator and then using Mawhin’s continuation theorem, some new results on the existence of periodic solutions are obtained. [Copyright &y& Elsevier]

Abstract: Using inequality techniques and coincidence degree theory, new results are provided concerning the existence of -periodic solutions for fourth-order nonlinear differential equations. Two illustrative examples are provided to demonstrate that the results in this paper hold under weaker conditions than the existing ones, and are more effective. [Copyright &y& Elsevier]

Abstract: In this paper, using Mawhin’s continuation theorem, we obtain existence results concerning -periodic solutions of fourth-order nonlinear differential equations of the type where , is continuous, -periodic in and is continuous, -periodic with mean value zero. Applications are given for the extended Fisher–Kolmogorov and Swift–Hohenberg equations with forcing term. [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]

Abstract: By means of Mawhin’s continuation theorem, existence criteria is established for the periodic solutions to a neutral equation with variable parameter. It is worth stating that the coefficient is not a constant, which is different from the corresponding ones of past work. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a general high-order delay differential equation in the following form: where is a continuous periodic function defined on with period ; is a continuous function defined on and periodic to , for all . By applying Mawhin’s continuation theorem and a new inequality established in this paper, we obtain sufficient conditions for the existence of periodic solutions for the equation. Our results are new and the methods are different from previous works. Moreover, an example to illustrate the results is given. [Copyright &y& Elsevier]

Abstract: By means of Mawhin’s continuation theorem, a class of p-Laplacian type differential equation with a deviating argument of the form is studied. A new result, related to and the deviating argument , is obtained. It is significant that the growth degree with respect to the variable in is allowed to be greater than , which could be achieved infrequently in previous papers. [Copyright &y& Elsevier]

Abstract: In this paper, by utilizing Mawhin’s continuation theorem and constructing suitable Lyapunov functional, a Volterra model with mutual interference and Holling II type functional response is studied. Some sufficient conditions are obtained for the existence, uniqueness and global attractivity of positive periodic solution of the model. Furthermore, the conditions are related to the interference constant m and an example is illustrated to verify the results by using Maple. [Copyright &y& Elsevier]

By means of Mawhin’s continuation theorem, a second order differential equation with a deviating argument is studied. A new result on the existence of periodic solutions is obtained. Meanwhile, the approaches used to estimate a priori bounds of periodic solutions are different from the corresponding ones in the known literature. [ABSTRACT FROM AUTHOR]