Results 21 to 30 of about 12,047 (285)

Existence of infinitely many solutions for semilinear elliptic equations

Electronic Journal of Differential Equations, 2016
In this article, we study the existence and infinitely many solutions for the elliptic boundary-value problem $$\displaylines{ -\Delta u+a(x)u=f(x,u) \quad\text{in }\Omega, \cr u=0 \quad\text{on }\partial\Omega.
Hui-Lan Pan, Chun-Lei Tang
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Infinitely many positive solutions of nonlinear Schrödinger equations [PDF]

Calculus of Variations and Partial Differential Equations, 2021
AbstractThe paper deals with the equation $$-\Delta u+a(x) u =|u|^{p-1}u $$ - Δ u + a ( x ) u
Molle R., Passaseo D.
openaire   +6 more sources

A variational approach for mixed elliptic problems involving the p-Laplacian with two parameters

Boundary Value Problems, 2022
By exploiting an abstract critical-point result for differentiable and parametric functionals, we show the existence of infinitely many weak solutions for nonlinear elliptic equations with nonhomogeneous boundary conditions. More accurately, we determine
Armin Hadjian, Juan J. Nieto
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Infinitely many solutions of degenerate quasilinear Schrödinger equation with general potentials

Boundary Value Problems, 2021
In this paper, we study the following quasilinear Schrödinger equation: − div ( a ( x , ∇ u ) ) + V ( x ) | x | − α p ∗ | u | p − 2 u = K ( x ) | x | − α p ∗ f ( x , u ) in  R N , $$ -\operatorname{div}\bigl(a(x,\nabla u)\bigr)+V(x) \vert x \vert ...
Yan Meng, Xianjiu Huang, Jianhua Chen
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INFINITELY MANY SOLUTIONS FOR A NONLOCAL PROBLEM

Journal of Applied Analysis & Computation, 2020
Summary: Consider a class of nonlocal problems \[ \begin{cases} -(a-b\int_{\Omega}|\nabla u|^2dx)\Delta u= f(x,u),\quad &x \in\Omega, \\ u=0, & x \in\partial\Omega, \end{cases} \] where \(a>0\), \(b>0\), \(\Omega\subset \mathbb{R}^N\) is a bounded open domain, \(f:\overline{\Omega} \times \mathbb R \longrightarrow \mathbb R\) is a Carathéodory function.
Tang, Zhiyun, Ou, Zengqi
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Infinitely many solutions for a boundary Yamabe problem

Nonlinear Differential Equations and Applications NoDEA
We consider the classical geometric problem of prescribing the scalar and the boundary mean curvature problem in the unit ball Bn endowed with the standard Euclidean metric. We will deal with the case of negative scalar curvature showing the existence of
Pu, Yixing, Battaglia, Luca, Vaira, Giusi   +2 more
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Infinitely many solutions for a gauged nonlinear Schrödinger equation with a perturbation

Nonlinear Analysis, 2021
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 ...
Jiafa Xu, Jie Liu, Donal O'Regan
doaj   +1 more source

A sequence of positive solutions for sixth-order ordinary nonlinear differential problems

Electronic Journal of Qualitative Theory of Differential Equations, 2021
Infinitely many solutions for a nonlinear sixth-order differential equation are obtained. The variational methods are adopted and an oscillating behaviour on the nonlinear term is required, avoiding any symmetry assumption.
Gabriele Bonanno, Roberto Livrea
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Infinitely many solutions for nonhomogeneous Choquard equations

Electronic Journal of Qualitative Theory of Differential Equations, 2019
In this paper, we study the following nonhomogeneous Choquard equation \begin{equation*} \begin{split} -\Delta u+V(x)u=(I_\alpha*|u|^p)|u|^{p-2}u+f(x),\qquad x\in \mathbb{R}^N, \end{split} \end{equation*} where $N\geq3,\alpha\in(0,N),p\in \big[\frac{N ...
Tao Wang, Hui Guo
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Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation [PDF]

, 2008
The Yablonskii-Vorob'ev polynomials yn(t), which are defined by a second order bilinear differential-difference equation, provide rational solutions of the Toda lattice.
Common, Alan K., Hone, Andrew N.W.
core   +1 more source