On Existence of L<sup>∞</sup>-Ground States for Singular Elliptic Equations in the Presence of a Strongly Nonlinear Term

Gonçalves, J. V.; Melo, A. L.; Santos, Carlos Alberto

doi:10.1515/ans-2007-0308

Cited by 25 publications

(8 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The main objective of this paper is to improve the principal result of Yang and Xu 7 and to complement other works see, e.g., [8][9][10][11][12][13][14][15][16][17][18][19][20] and references therein for more general nonlinearities in the terms f and g which include the cases considered by them.…”

Section: Introductionmentioning

confidence: 90%

Entire Solutions for a Quasilinear Problem in the Presence of Sublinear and Super-Linear Terms

Santos

2009

Boundary Value Problems

View full text Add to dashboard Cite

We establish new results concerning existence and asymptotic behavior of entire, positive, and bounded solutions which converge to zero at infinite for the quasilinear equation −Δ p u a x f u λb x g u , x ∈ R N , 1 < p < N, where f, g : 0, ∞ → 0, ∞ are suitable functions and a x , b x ≥ 0 are not identically zero continuous functions. We show that there exists at least one solution for the above-mentioned problem for each 0 ≤ λ < λ , for some λ > 0. Penalty arguments, variational principles, lower-upper solutions, and an approximation procedure will be explored.

show abstract

Section: Introductionmentioning

confidence: 90%

Entire Solutions for a Quasilinear Problem in the Presence of Sublinear and Super-Linear Terms

Santos

2009

Boundary Value Problems

View full text Add to dashboard Cite

show abstract

“…The proof of Theorem 2.1 is based in part on arguments in [6,22]. At first we state a variant of a result in [23].…”

Section: Upper Solutions Decaying To Zeromentioning

confidence: 99%

Existence and nonexistence of ground state solutions for elliptic equations with a convection term

Gonçalves

Silva

2010

Nonlinear Analysis: Theory, Methods & Applications

Self Cite

View full text Add to dashboard Cite

“…We [35] obtained the existence, uniqueness, and asymptotical behavior of solutions to a Choquard equation with singularity. For more related topics, one can see [12,17,27] and the references cited therein.…”

Section: Introduction Nonlinear Equations Involving Fractional Powermentioning

confidence: 99%

Fractional Schrödinger–poisson System With Singularity: Existence, Uniqueness, and Asymptotic Behavior

Chen²

2020

Glasgow Math. J.

View full text Add to dashboard Cite

In this paper, we consider the following fractional Schrödinger–Poisson system with singularity \begin{equation*} \left \{\begin{array}{lcl} ({-}\Delta)^s u+V(x)u+\lambda \phi u = f(x)u^{-\gamma}, &&\quad x\in\mathbb{R}^3,\\ ({-}\Delta)^t \phi = u^2, &&\quad x\in\mathbb{R}^3,\\ u>0,&&\quad x\in\mathbb{R}^3, \end{array}\right. \end{equation*} where 0 < γ < 1, λ > 0 and 0 < s ≤ t < 1 with 4s + 2t > 3. Under certain assumptions on V and f, we show the existence, uniqueness, and monotonicity of positive solution uλ using the variational method. We also give a convergence property of uλ as λ → 0, when λ is regarded as a positive parameter.

show abstract

On Existence of L^∞-Ground States for Singular Elliptic Equations in the Presence of a Strongly Nonlinear Term

Abstract: We establish new results concerning existence and the behavior at infinity of solutions for the singular nonlinear elliptic equation −Δu = ρa(x)u

Cited by 25 publications

References 1 publication

Entire Solutions for a Quasilinear Problem in the Presence of Sublinear and Super-Linear Terms

Entire Solutions for a Quasilinear Problem in the Presence of Sublinear and Super-Linear Terms

Existence and nonexistence of ground state solutions for elliptic equations with a convection term

Fractional Schrödinger–poisson System With Singularity: Existence, Uniqueness, and Asymptotic Behavior

Contact Info

Product

Resources

About

On Existence of L∞-Ground States for Singular Elliptic Equations in the Presence of a Strongly Nonlinear Term

Abstract: We establish new results concerning existence and the behavior at infinity of solutions for the singular nonlinear elliptic equation −Δu = ρa(x)u

Cited by 25 publications

References 1 publication

Entire Solutions for a Quasilinear Problem in the Presence of Sublinear and Super-Linear Terms

Entire Solutions for a Quasilinear Problem in the Presence of Sublinear and Super-Linear Terms

Existence and nonexistence of ground state solutions for elliptic equations with a convection term

Fractional Schrödinger–poisson System With Singularity: Existence, Uniqueness, and Asymptotic Behavior

Contact Info

Product

Resources

About

On Existence of L^∞-Ground States for Singular Elliptic Equations in the Presence of a Strongly Nonlinear Term