182 research outputs found

### Periodic solutions for second-order Hamiltonian systems with a p-Laplacian

In this paper, by using the least action principle, Sobolev’s inequality and Wirtinger’s inequality, some existence theorems are obtained for periodic solutions of second-order Hamiltonian systems with a p-Laplacian under subconvex condition, sublinear growth condition and linear growth condition. Our results generalize and improve those in the literature

### Periodic solutions for a kind of Rayleigh equation with a deviating argument

AbstractExistence of periodic solutions for a kind of Rayleigh equation with a deviating argument x″(t)+f(x′(t))+g(x(t−τ(t)))=p(t) is studied, and some new results are obtained. Our work generalizes and improves the known results in the literature

### Ground state solutions for a class of nonlinear Maxwell-Dirac system

This paper is concerned with the following nonlinear Maxwell-Dirac system\begin{equation*}\begin{cases}\displaystyle-i\sum^{3}_{k=1}\alpha_{k}\partial_{k}u + a\beta u + \omega u-\phi u =F_{u}(x,u),\\-\Delta \phi=4\pi|u|^{2,\\\end{cases} \end{equation*}for $x\in\R^{3}$. The Dirac operator is unbounded from below and above, so the associated energy functional is strongly indefinite. We use the linking and concentration compactness arguments to establish the existence of ground state solutionsfor this system with asymptotically quadratic nonlinearity

### Global asymptotic behavior and boundedness of positive solutions to an odd-order rational difference equation

AbstractIn this note we consider the following high-order rational difference equation xn=1+∏i=1k(1−xn−i)∑i=1kxn−i,n=0,1,…, where k≥3 is odd number, x−k,x−k+1,x−k+2,…,x−1 is positive numbers. We obtain the boundedness of positive solutions for the above equation, and with the perturbation of initial values, we mainly use the transformation method to prove that the positive equilibrium point of this equation is globally asymptotically stable

### A Note on the Normal Index and the c

Let M be a maximal subgroup of finite group G. For each chief factor H/K of G such that K≤M and G=MH, we called the order of H/K the normal index of M and M∩H/K a section of M in G. Using the concepts of normal index and c-section, we obtain some new characterizations of p-solvable, 2-supersolvable, and p-nilpotent

### Ground state sign-changing solutions for Kirchhoff equations with logarithmic nonlinearity

In this paper, we study Kirchhoff equations with logarithmic nonlinearity:
\begin{equation*}
\begin{cases}
-(a+b\int_\Omega|\nabla u|^2)\Delta u+ V(x)u=|u|^{p-2}u\ln u^2, & \mbox{in}\ \Omega,\\
u=0,& \mbox{on}\ \partial\Omega,
\end{cases}
\end{equation*}
where $a,b>0$ are constants, $4<p<2^*$, $\Omega$ is a smooth bounded domain of $\mathbb{R}^3$ and $V:\Omega\to\mathbb{R}$. Using constraint variational method, topological degree theory and some new energy estimate inequalities, we prove the existence of ground state solutions and ground state sign-changing solutions with precisely two nodal domains. In particular, some new tricks are used to overcome the difficulties that $|u|^{p-2}u\ln u^2$ is sign-changing and satisfies neither the monotonicity condition nor the Ambrosetti–Rabinowitz condition

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