Nodal solutions for logarithmic weighted N-laplacian problem with exponential nonlinearities

Brahim, Dridi,; Jaidane, Rached

doi:10.1007/s11565-023-00457-6

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…To be more specific, the authors demonstrated the existence of positive solutions for the above problem by combining variational techniques with regularity arguments. Alternatively, [4,10,11,14,19,20,43] investigated elliptic equations with weighted N-Laplacian operator and critical Trudinger-Moser nonlinearities, while this paper will focus on a different class of problems.…”

Section: Introductionmentioning

confidence: 99%

Least energy nodal solutions for a weighted $(N, p)$-Schrödinger problem involving a continuous potential under exponential growth nonlinearity

Baraket,

Dridi,

Grine

et al. 2024

Bound Value Probl

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This article aims to investigate the existence of nontrivial solutions with minimal energy for a logarithmic weighted $(N,p)$ ( N , p ) -Laplacian problem in the unit ball B of $\mathbb{R}^{N}$ R N , $N>2$ N > 2 . The nonlinearities of the equation are critical or subcritical growth, which is motivated by weighted Trudinger–Moser type inequalities. Our approach is based on constrained minimization within the Nehari set, the quantitative deformation lemma, and degree theory results.

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Section: Introductionmentioning

confidence: 99%

Least energy nodal solutions for a weighted $(N, p)$-Schrödinger problem involving a continuous potential under exponential growth nonlinearity

Baraket,

Dridi,

Grine

et al. 2024

Bound Value Probl

Self Cite

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“…The existence of solutions to nonlinear weighted elliptic equations involving subcritical and critical growth of the logarithmic weighted Trudinger-Moser type or weighted Adam's inequalities has been studied extensively in recent years, motivated by its applicability in many fields of modern mathematics; see ( [1,8,14,27,28,32]) for a survey on this subject.…”

Section: Introductionmentioning

confidence: 99%

Weigthed elliptic equation of Kirchhoff type with exponential non linear growthWeigthed elliptic equation of Kirchhoff type with exponential non linear growth

Jaidane

2022

AUCMCS

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"This work is concerned with the existence of a positive ground state solution for the following non local weighted problem \begin{equation*} \displaystyle \left\{ \begin{array}{rclll} L_{(\sigma,V)}u &= & \displaystyle f(x,u)& \mbox{in} \ B \\ u &>&0 &\mbox{in }B\\ u&=&0 &\mbox{on } \partial B, \end{array} \right. \end{equation*} where $$L_{(\sigma,V)}u:=g(\int_{B}(\sigma(x)|\nabla u|^{N}+V(x)|u|^{N})dx)\big[-\textmd{div} (\sigma(x)|\nabla u|^{N-2} \nabla u)+V(x)|u|^{N-2}u\big],$$ B is the unit ball of $\mathbb{R}^{N}$, $ N>2$, $\sigma(x)=\Big(\log(\frac{e}{|x|})\Big)^{\beta(N-1)}$, $\beta \in[0,1)$ the singular logarithm weight , $V(x)$ is a positif continuous potential.The Kirchhoff function $g$ is positive and continuous on $(0,+\infty)$. The nonlinearities are critical or subcritical growth in view of Trudinger-Moser inequalities of exponential type. We prove the existence of a positive ground state solution by using Mountain Pass theorem . In the critical case, the Euler-Lagrange function loses compactness except for a certain level. We dodge this problem by using adapted test functions to identify this level of compactness."

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Sign-changing solutions for a weighted Kirchhoff problem with exponential growth non-linearity

Dridi,

Amor Ben Ali,

Jaidane

2024

Complex Variables and Elliptic Equations

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Nodal solutions for logarithmic weighted N-laplacian problem with exponential nonlinearities

Cited by 3 publications

References 14 publications

Least energy nodal solutions for a weighted $(N, p)$-Schrödinger problem involving a continuous potential under exponential growth nonlinearity

Least energy nodal solutions for a weighted $(N, p)$-Schrödinger problem involving a continuous potential under exponential growth nonlinearity

Weigthed elliptic equation of Kirchhoff type with exponential non linear growthWeigthed elliptic equation of Kirchhoff type with exponential non linear growth

Sign-changing solutions for a weighted Kirchhoff problem with exponential growth non-linearity

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