Positive Solutions of a Nonlocal and Nonvariational Elliptic Problem

2021 ◽  
Vol 41 (5) ◽  
pp. 1764-1776
Author(s):  
Lingjun Liu ◽  
Feilin Shi
Keyword(s):  
Positive Solutions ◽  
Elliptic Problem

Positive solutions to a supercritical elliptic problem that concentrate along a thin spherical hole

2015 ◽  
Vol 126 (1) ◽  
pp. 341-357 ◽  
Author(s):  
Mónica Clapp ◽  
Jorge Faya ◽  
Angela Pistoia
Keyword(s):  
Positive Solutions ◽  
Elliptic Problem

NONNEGATIVE SOLUTIONS FOR INDEFINITE SUBLINEAR ELLIPTIC PROBLEMS

2012 ◽  
Vol 14 (03) ◽  
pp. 1250021 ◽  
Author(s):  
FRANCISCO ODAIR DE PAIVA
Keyword(s):  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Solution Method ◽  
Mountain Pass Theorem ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Nonnegative Solutions ◽  
Carathéodory Function ◽  
Multiplicity Of Positive Solutions

This paper is devoted to the study of existence, nonexistence and multiplicity of positive solutions for the semilinear elliptic problem [Formula: see text] where Ω is a bounded domain of ℝN, λ ∈ ℝ and g(x, u) is a Carathéodory function. The obtained results apply to the following classes of nonlinearities: a(x)uq + b(x)up and c(x)(1 + u)p (0 ≤ q < 1 < p). The proofs rely on the sub-super solution method and the mountain pass theorem.

MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS ASSOCIATED TO A CLASS OF p-LAPLACIAN LIKE OPERATORS

2003 ◽  
Vol 05 (05) ◽  
pp. 737-759 ◽  
Author(s):  
NOBUYOSHI FUKAGAI ◽  
KIMIAKI NARUKAWA
Keyword(s):  
Positive Solutions ◽  
Elliptic Problem ◽  
Eigenvalue Problems ◽  
Multiple Positive Solutions ◽  
Combined Effects ◽  
Nonlinear Eigenvalue Problems ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic ◽  
Nonlinear Eigenvalue

This paper deals with positive solutions of a class of nonlinear eigenvalue problems. For a quasilinear elliptic problem (#) - div (ϕ(|∇u|)∇u) = λf(x,u) in Ω, u = 0 on ∂Ω, we assume asymptotic conditions on ϕ and f such as ϕ(t) ~ tp0-2, f(x,t) ~ tq0-1as t → +0 and ϕ(t) ~ tp1-2, f(x,t) ~ tq1-1as t → ∞. The combined effects of sub-nonlinearity (p0> q0) and super-nonlinearity (p1< q1) with the subcritical term f(x,u) imply the existence of at least two positive solutions of (#) for 0 < λ < Λ.

scholarly journals On the number of positive solutions of a quasilinear elliptic problem

2006 ◽  
Vol 55 (6) ◽  
pp. 1835-1856 ◽  
Author(s):  
Marcelo Furtado ◽  
Giovany Malcher Figueiredo
Keyword(s):  
Positive Solutions ◽  
Elliptic Problem ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic

scholarly journals Existence of Multiple Solutions for a -Kirchhoff Problem with Nonlinear Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zonghu Xiu ◽  
Caisheng Chen
Keyword(s):  
Variational Method ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Nehari Manifold ◽  
The Nehari Manifold ◽  
Kirchhoff Problem

The paper considers the existence of multiple solutions of the singular nonlocal elliptic problem , ,   = , on , where , . By the variational method on the Nehari manifold, we prove that the problem has at least two positive solutions when some conditions are satisfied.

Multiplicity and nondegeneracy of positive solutions to quasilinear equations on compact Riemannian manifolds

2015 ◽  
Vol 17 (02) ◽  
pp. 1450029 ◽  
Author(s):  
Silvia Cingolani ◽  
Giuseppina Vannella ◽  
Daniela Visetti
Keyword(s):  
Riemannian Manifold ◽  
Positive Solutions ◽  
Riemannian Manifolds ◽  
Elliptic Problem ◽  
Quasilinear Equations ◽  
Metric Tensor ◽  
Poincaré Polynomial ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Problem ◽  
Quasilinear Elliptic

We consider a compact, connected, orientable, boundaryless Riemannian manifold (M, g) of class C∞ where g denotes the metric tensor. Let n = dim M ≥ 3. Using Morse techniques, we prove the existence of [Formula: see text] nonconstant solutions u ∈ H1,p(M) to the quasilinear problem [Formula: see text] for ε > 0 small enough, where 2 ≤ p < n, p < q < p*, p* = np/(n - p) and [Formula: see text] is the p-laplacian associated to g of u (note that Δ2,g = Δg) and [Formula: see text] denotes the Poincaré polynomial of M. We also establish results of genericity of nondegenerate solutions for the quasilinear elliptic problem (Pε).

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