Explanipedia

POSITIVE RADIAL SOLUTIONS FOR A SEMIPOSITONE PROBLEM OF ELLIPTIC KIRCHHOFF EQUATIONS WITH SUBLINEAR NONLINEARITIES Open

Tingting Zhang, Ruyun Ma, Meng Yan · 2025

Global structure of positive and sign-changing periodic solutions for the equations with Minkowski-curvature operator Open

Ruyun Ma, Zhongzi Zhao, Xiaoxiao Su · 2024

We show the existence of unbounded connected components of 2π-periodic positive solutions for the equations with one-dimensional Minkowski-curvature operator − u ′ 1 − u ′ 2 ′ = λ a ( x ) f ( u , u …

Global bifurcation of positive solutions for a superlinear p-Laplacian system Open

Lijuan Yang, Ruyun Ma · 2024

We are concerned with the principal eigenvalue of (P) { − Δ p u = λ θ 1 φ p ( v ) , x ∈ Ω , − Δ p v = λ θ 2 φ p ( u ) , x ∈ Ω , u = 0 = v , x ∈ ∂ Ω and the global structure of positive solutio…

INFINITELY MANY SOLUTIONS FOR A P-SUPERLINEAR P-LAPLACIAN PROBLEMS Open

Lijuan Yang, Ruyun Ma · 2024

We are concerned with the existence of infinitely many solutions for -Laplacian problem $ \left\{\begin{array}{l}-\left(\varphi_p\left(u^{\prime}\right)\right)^{\prime}=g(u)+h\left(x, u, u^{\prime}\right), \quad x \in(0,1), \\u(0)=u(1)=0,\…

GLOBAL STRUCTURE OF POSITIVE SOLUTIONS FOR FIRST-ORDER DISCRETE PERIODIC BOUNDARY VALUE PROBLEMS WITH INDEFINITE WEIGHT Open

Xiaoxiao Su, Meng Yan, Ruyun Ma · 2023

We are concerned with the first-order discrete periodic boundary value problem $ \begin{align} \left\{\begin{array}{ll} -D u(t)= \lambda a(t) f(u(t)),\; \; \; t\in\{1,2,\cdots,T\},\\ u(0)=u(T), \end{array} \right.\;\;\;\;\;\;\;\;\;\;\;\;\;…

Infinitely many radial solutions of superlinear elliptic problems with dependence on the gradient terms in an annulus Open

Yan Zhu, Ruyun Ma, Xiaoxiao Su · 2023

In this paper, we are concerned with elliptic problems $$ \textstyle\begin{cases} -\Delta u= f(u)+ g( \vert x \vert ,u,\frac{x}{ \vert x \vert }\cdot \nabla u),&x\in \Omega , \\ u|_{\partial \Omega}=0, \end{cases} $$ …

Infinitely many solutions of p-superlinear p-Laplacian problems Open

Ruyun Ma, Lijuan Yang · 2023

We are concerned with the existence of infinitely many solutions for p-Laplacian problem \begin{equation*}\left\{ \begin{array}{ll} -(\varphi_p(u'))'= g(u)+h(x,u,u'), &x\in(0,1),\ \ \\ u(0)=u(1)=0, \ \ \end{array} \right.\eqno(P)\end{equat…

NON-SPURIOUS SOLUTIONS OF DISCRETE MIXED BOUNDARY VALUE PROBLEM WITH SINGULAR ϕ-LAPLACIAN Open

Man Xu, Ruyun Ma, Ting Wang · 2023

In this paper, we consider the differential and difference problems associated with the discrete approximation of classical radial solutions of the nonlinear Dirichlet problem for the prescribed mean curvature equation in Minkowski space \…

Global bifurcation of positive solutions for a class of superlinear elliptic systems Open

Ruyun Ma, Yan Zhu, Yali Zhang · 2023

We are concerned with the global bifurcation of positive solutions for semilinear elliptic systems of the form where is the bifurcation parameter, , is a bounded domain wi…

Neumann problems of superlinear elliptic systems at resonance Open

Ruyun Ma, Zhongzi Zhao, Mantang Ma · 2022

We prove existence of weak solutions of Neumann problem of nonhomogeneous elliptic system with asymmetric nonlinearities that may resonant at and superlinear at . The proof is based on Mawhin's coincidence theory and the product formu…

Ambrosetti-Prodi-type results for a class of difference equations with nonlinearities indefinite in sign Open

Jiao Zhao, Ruyun Ma · 2022

In this article, we are concerned with the periodic solutions of first-order difference equation Δ u ( t − 1 ) = f ( t , u ( t ) ) − s , t ∈ Z , ( P ) \Delta u\left(t-1)=f\left(t,u\left(t))-s,\hspace{1em}t\in {\mathbb{…

Existence and multiplicity of solutions for second-order Dirichlet problems with nonlinear impulses Open

Mantang Ma, Ruyun Ma · 2022

We are concerned with Dirichlet problems of impulsive differential equations − u ″ ( x ) − λ u ( x ) + g ( x , u ( x ) ) + ∑ j = 1 p I j ( u ( x ) ) δ ( x − y j ) = f ( x )…

ON A SUPERLINEAR SECOND ORDER ELLIPTIC PROBLEM AT RESONANCE Open

Ruyun Ma, Zhongzi Zhao, Mantang Ma · 2022

We show the existence of solutions of the superlinear problem $ \begin{equation*} \begin{aligned} &-\Delta u=\lambda_1 u +f(u^+)+h(x),&&{\rm{in}} \ \Omega,\\ &u=0, && {\rm{on}} \ \partial\Omega, \end{aligned} \end{equation*} $ where $ \Om…

Connected components of positive solutions of biharmonic equations with the clamped plate conditions in two dimensions Open

Ruyun Ma, Zhongzi Zhao, Dongliang Yan · 2021

This article concerns the clamped plate equation $$\displaylines{ \Delta^2 u=\lambda a(x)f(u), \quad \text{in } \Omega,\cr u=\frac {\partial u}{\partial \nu}= 0 \quad \text{on } \partial \Omega, }$$ where $\Omega$ is a bounded domain in …

EXISTENCE AND MULTIPLICITY OF SIGN-CHANGING SOLUTIONS FOR THE DISCRETE PERIODIC PROBLEMS WITH MINKOWSKI-CURVATURE OPERATOR Open

Zhongzi Zhao, Ruyun Ma, Yan Zhu · 2021

We are concerned with the discrete periodic problems with Minkowski-curvature operator \begin{document} $ \left\{\begin{array}{l} -\nabla(\frac{\Delta u(t)}{\sqrt{1-(\Delta u(t))^2}}) = \lambda g(t, u(t)), \quad t\in \mathbb{T}, \\ u(0) …

MULTIPLE POSITIVE SOLUTIONS OF THE DISCRETE DIRICHLET PROBLEM WITH ONE-DIMENSIONAL PRESCRIBED MEAN CURVATURE OPERATOR Open

Yanqiong Lu, Ruyun Ma · 2020

We shall discuss the existence and multiplicity of positive solutions for the discrete Dirichlet problem with one-dimensional prescribed mean curvature operator. Based on the critical point theory, we shall show the existence of either on…

Multiple positive solutions of second-order nonlinear difference equations with discrete singular ϕ-Laplacian Open

Xiaoxiao Su, Ruyun Ma · 2020

Nonlinear polyharmonic problems with the parameter near resonance Open

Ruyun Ma, Xiaoxiao Su, Dongliang Yan · 2020

This paper is concerned with sublinear perturbations of resonant linear polyharmonic problems. We establish some {\it a priori} bounds and use these together with Leray-Schauder continuation and bifurcation arguments to obtain extensions o…

Global continuum and multiple positive solutions to one-dimensional p-Laplacian boundary value problem Open

Liping Wei, Ruyun Ma · 2020

We show the global structure of the set of positive solutions of a discrete Dirichlet problem involving the p -Laplacian difference operator suggesting suitable conditions on the weight function and nonlinearity. We obtain existence and mu…

Bifurcation Behaviors of Steady-State Solution to a Discrete General Brusselator Model Open

Ruyun Ma, Zhongzi Zhao · 2020

We study the local and global bifurcation of nonnegative nonconstant solutions of a discrete general Brusselator model. We generalize the linear in the standard Brusselator model to the nonlinear . Assume that is a strictly increasing fu…

Global structure of one-sign solutions for a simply supported beam equation Open

Dongliang Yan, Ruyun Ma, Xiaoxiao Su · 2020

In this paper, we consider the nonlinear eigenvalue problem $$\begin{gathered} u''''= \lambda h(t)f(u),\quad 0< t< 1, \\ u(0)=u(1)=u''(0)=u''(1)=0, \\ \end{gathered} $$ where $h\in C([0,1], (0,\infty))$ ; $f\in C(\mathbb{R},\mathbb{R})$ …

Positive solutions for some discrete semipositone problems via bifurcation theory Open

Man Xu, Ruyun Ma · 2020

Let $T > 1$ be an integer, and let $\mathbb{T}=\{1, 2,\ldots ,T\}$ . We show the existence of positive solutions of the Dirichlet boundary value problem with second-order difference operator $$ \textstyle\begin{cases} -\triangle ^{2} u(j…

Global structure of sign-changing solutions for discrete Dirichlet problems Open

Liping Wei, Ruyun Ma · 2020

Let T > 1 T\gt 1 be an integer, T ≔ [ 1 , T ] Z = { 1 , 2 , … , T } , T ˆ ≔ { 0 , 1 , … , T + 1 } {\mathbb{T}}:= {{[}1,T]}_{{\mathbb{Z}}}=\{1,2,\ldots ,T\},\hspace{.0em}\hat{{\mathbb{T}}}:= \{0,1,\ldots ,T+1\} . In this articl…

THREE RADIAL POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS IN Open

Suyun Wang, Yanhong Zhang, Ruyun Ma · 2020

This paper is concerned with the semilinear elliptic problem $\left\{ \begin{matrix} -\Delta u=\lambda h(|x|)f(u)\ \ \ \ \ \ \ \ \ \ \ \ \ \text{in}\ {{\mathbb{R}}^{N}}, \ u\left( x \right)>0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ …

Disconjugacy conditions and spectrum structure of clamped beam equations with two parameters Open

Yanqiong Lu, Ruyun Ma · 2020

In this work, we apply the 'disconjugacy theory' and Elias's spectrum theory to study the disconjugacy $ u^{(4)} + \beta u''-\alpha u = 0 $ with two parameters $ \alpha,\beta\in\mathbb{R} $ and the spectrum structure of the linear operator…

Multiplicity of nodal solutions for fourth order equation with clamped beam boundary conditions Open

Ruyun Ma, Dongliang Yan, Liping Wei · 2020

In this paper, we study the global structure of nodal solutions of $$ \begin{cases} u''''(x)=\lambda h(x)f(u(x)), & 0 0$ is a parameter, $h\in C([0,1],(0, \infty))$, $f\in C…

Global bifurcation of sign-changing radial solutions of elliptic equations of order 2m in annular domains Open

Ruyun Ma, Dongliang Yan, Liping Wei · 2020

In this paper we study the global bifurcation of sign-changing radial solutions for some semilinear elliptic problems of order 2m in an annulus with Dirichlet boundary conditions.

Existence of infinitely many radial nodal solutions for a Dirichlet problem involving mean curvature operator in Minkowski space Open

Man Xu, Ruyun Ma · 2020

In this paper, we show the existence of infinitely many radial nodal solutions for the following Dirichlet problem involving mean curvature operator in Minkowski space \begin{equation*} \begin{cases} -\text{div}\left(\frac{\nabla y}{\sqrt{…

Local and global bifurcation of steady states to a general Brusselator model Open

Zhongzi Zhao, Ruyun Ma · 2019

In this paper, we consider the local and global bifurcation of nonnegative nonconstant solutions of a general Brusselator model $$ \textstyle\begin{cases} -d_{1}\triangle u=a-(b+1)f(u)+u^{2}v, & x\in \varOmega , \\ -d_{2}\triangle v=bf(u)-…

S-shaped connected component of radial positive solutions for a prescribed mean curvature problem in an annular domain Open

Man Xu, Ruyun Ma · 2019

In this paper, we show the existence of an S -shaped connected component in the set of radial positive solutions of boundary value problem $$\begin{array}{} \displaystyle \left\{\,\begin{array}{} -\text{ div}\big(\phi_N(\nabla y)\big)=\lam…

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