Positive solutions for a system of nnth-order nonlinear boundary value problems

In this paper, we investigate the existence, multiplicity and uniqueness of positive solutions for the following system of $n$th-order nonlinear boundary value problems $$\begin{cases} u^{(n)}(t)+f(t,u(t),v(t))=0,0<t<1,\\v^{(n)}(t)+g(t,u(t),v(t))=0, 0<t<1,\\ u(0)=u'(0)=\ldots=u^{(n-2)}(0)=u(1)=0,\\ v(0)= v'(0)=\ldots=v^{(n-2)}(0)=v(1)=0. \end{cases}$$ Based on a priori estimates achieved by using Jensen's integral inequality, we use fixed point index theory to establish our main results. Our assumptions on the nonlinearities are mostly formulated in terms of spectral radii of associated linear integral operators. In addition, concave and convex functions are utilized to characterize coupling behaviors of $f$ and $g$, so that we can treat the three cases: the first with both superlinear, the second with both sublinear, and the last with one superlinear and the other sublinear

Positive solutions for a class of fractional boundary value problems

In this work, by virtue of the Krasnoselskii–Zabreiko fixed point theorem, we investigate the existence of positive solutions for a class of fractional boundary value problems under some appropriate conditions concerning the first eigenvalue of the relevant linear operator. Moreover, we utilize the method of lower and upper solutions to discuss the unique positive solution when the nonlinear term grows sublinearly

Solutions for a fractional difference boundary value problem

Using a variational approach and critical point theory, we investigate the existence of solutions for a fractional difference boundary value problem

Infinitely many solutions for a gauged nonlinear Schrödinger equation with a perturbation

In this paper, we use the Fountain theorem under the Cerami condition to study the gauged nonlinear Schrödinger equation with a perturbation in R2. Under some appropriate conditions, we obtain the existence of infinitely many high energy solutions for the equation

Solvability for a Hadamard-type fractional integral boundary value problem

In this paper, we study an integral boundary value problem involving a Hadamard-type fractional differential equation. Using fixed point theory and upper-lower solutions, we present some sufficient conditions to obtain existence theorems of positive solutions for the problem. Examples are provided to illustrate our results

Stationary solutions for a generalized Kadomtsev-Petviashvili equation in bounded domain

In this work, we are mainly concerned with the existence of stationary solutions for the generalized Kadomtsev-Petviashvili equation in bounded domain in $\mathbb{R}^n$ $$\left\{\begin{aligned} &\frac{\partial^3}{\partial x^3}u(x,y)+\frac{\partial}{\partial x}f(u(x,y))=D_x^{-1}\Delta_yu(x,y),\ \text{in}\ \Omega,\\ &D_x^{-1}u|_{\partial\Omega}=0,\ u|_{\partial\Omega}=0, \end{aligned}\right.$$ where $\Omega\in \mathbb{R}^n$ is a bounded domain with smooth boundary $\partial\Omega$. We utilize critical point theory to establish our main results

Solvability for a system of Hadamard fractional multi-point boundary value problems

In this paper, we study a system of Hadamard fractional multi-point boundary value problems. We first obtain triple positive solutions when the nonlinearities satisfy some bounded conditions. Next, we also obtain a nontrivial solution when the nonlinearities can be asymptotically linear growth. Furthermore, we provide two examples to illustrate our main results

Weak Solutions for a -Laplacian Antiperiodic Boundary Value Problem with Impulsive Effects

By virtue of variational method and critical point theory, we will investigate the existence of weak solutions for a -Laplacian impulsive differential equation with antiperiodic boundary conditions

Positive solutions for a critical quasilinear Schrödinger equation

In our current work we investigate the following critical quasilinear Schrödinger equation $-\Delta \Theta+\mathcal V(x)\Theta-\Delta (\Theta^2)\Theta = |\Theta|^{22^*-2}\Theta+\lambda \mathcal K(x)g(\Theta), \ x \ \in \mathbb R^N,$ where $N\geq 3$, \lambda > 0 , $\mathcal V, \ \mathcal K\in C(\mathbb R^N, \mathbb R^+)$ and $g\in C(\mathbb R, \mathbb R)$ has a quasicritical growth condition. We use the dual approach and the mountain pass theorem to show that the considered problem has a positive solution when $\lambda$ is a large parameter