Existence and Nonexistence of Solutions to p-Laplacian Problems on Unbounded Domains

Jeong, Jeongmi; Kim, Chan-Gyun; Lee, Eun Kyoung

doi:10.3390/math7050438

Cited by 4 publications

(1 citation statement)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For ϕ(s) = |s| p−2 s with p > 1, the existence of positive solutions to problem (1) has been extensively studied in the literature for the past several decades (see References [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and references therein). For example, when p = 2, h is at most O(1/t 2−δ ) as t → 0 + for some δ > 0 and f (t, s) = e s , in Reference [3], it was shown that there exists λ 0 > 0 such that (1) has a positive solution for λ ∈ (0, λ 0 ) and it has no positive solution for λ > λ 0 .…”

Section: Remarkmentioning

confidence: 99%

Existence of Positive Solutions to Singular Boundary Value Problems Involving φ-Laplacian

Jeong

Kim

2019

Mathematics

Self Cite

View full text Add to dashboard Cite

This paper is concerned with the existence of positive solutions to singular Dirichlet boundary value problems involving φ -Laplacian. For non-negative nonlinearity f = f ( t , s ) satisfying f ( t , 0 ) ¬ ≡ 0 , the existence of an unbounded solution component is shown. By investigating the shape of the component depending on the behavior of f at ∞ , the existence, nonexistence and multiplicity of positive solutions are studied.

show abstract

Section: Remarkmentioning

confidence: 99%

Existence of Positive Solutions to Singular Boundary Value Problems Involving φ-Laplacian

Jeong

Kim

2019

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

Existence and Nonexistence of Solutions of Minkowski-Curvature Problems in Exterior Domains

Chen,

2024

The Quarterly Journal of Mathematics

View full text Add to dashboard Cite

In this paper, we show some nonexistence results of radial solutions for the following Minkowski curvature problems in an exterior domain: $$ \begin{cases} \ -\text{div} \big(\phi(\nabla v(x))\big)=k(x)f(v(x)), \quad\quad x\in\Omega,\\ \ v=0\ \text{on} \ \partial\Omega, \qquad\lim\limits_{x\rightarrow\infty}v(x)=0\\ \end{cases} $$ for R sufficiently large, where $\phi(s)=\frac{s}{\sqrt{1-s^{2}}}$ for $s\in{\mathbb R}$ with $s^2\lt1,$ $\Omega=\{x\in{{\mathbb R}^{N}}:\ |x| \gt R\}$, $N\geq3$ is an integer, $|\cdot|$ denotes the Euclidean norm on $\mathbb{R}^{N}$, R is a positive parameter, $f:\mathbb{R}\rightarrow\mathbb{R}$ is an odd and locally Lipschitz continuous function and $k \in C^{1}(\mathbb{R}^{+},\ \mathbb{R}^{+})$ with $\mathbb{R}^{+}=(0, +\infty)$. We also apply the fixed-point index theory to establish the existence of positive radial solutions of the above problems for R sufficiently small.

show abstract

The Existence of Positive Solutions to Quasilinear Differential Equation on Infinite Intervals

唐

2023

View full text Add to dashboard Cite

Existence and Nonexistence of Solutions to p-Laplacian Problems on Unbounded Domains

Abstract: In this article, using a fixed point index theorem on a cone, we prove the existence and multiplicity results of positive solutions to a one-dimensional p-Laplacian problem defined on infinite intervals. We also establish the nonexistence results of nontrivial solutions to the problem.

Cited by 4 publications

References 22 publications

Existence of Positive Solutions to Singular Boundary Value Problems Involving φ-Laplacian

Existence of Positive Solutions to Singular Boundary Value Problems Involving φ-Laplacian

Existence and Nonexistence of Solutions of Minkowski-Curvature Problems in Exterior Domains

The Existence of Positive Solutions to Quasilinear Differential Equation on Infinite Intervals

Contact Info

Product

Resources

About