The Nehari Manifold for p-Laplacian Equation with Dirichlet Boundary Condition [PDF]
Nonlinear Analysis, 2007 The Nehari manifold for the equation −∆pu(x) = λu(x)|u(x)| p−2 + b(x)|u(x)| γ−2u(x) for x ∈ Ω together with Dirichlet boundary condition is investigated in the case where 0 < γ < p.
G. A. Afrouzi, S. Mahdavi, Z. Naghizadeh
doaj +7 more sources
Some applications of the Nehari manifold method to functionals in $C^1(X \setminus \{0\})$ [PDF]
arXivGiven a real Banach space $X$, we show that the Nehari manifold method can be applied to functionals which are $C^1$ in $X \setminus \{0\}$. In particular we deal with functionals that can be unbounded near $0$, and prove the existence of a ground state and infinitely many critical points for such functionals.
Edir Júnior Ferreira Leite +2 more
arxiv +7 more sources
The Nehari manifold for aψ-Hilfer fractionalp-Laplacian
Applicable Analysis, 2021 In this paper, we discuss the existence and non-existence of weak solutions to the non-linear problem with a fractional p-Laplacian introduced by the ψ-Hilfer fractional operator, by combining the ...
J. Vanterler da C. Sousa +2 more
semanticscholar +6 more sources
Nehari manifold approach for superlinear double phase problems with variable exponents [PDF]
Annali di Matematica Pura ed Applicata (1923 -), 2023 AbstractIn this paper we consider quasilinear elliptic equations driven by the variable exponent double phase operator with superlinear right-hand sides. Under very general assumptions on the nonlinearity, we prove a multiplicity result for such problems whereby we show the existence of a positive solution, a negative one and a solution with changing ...
Ángel Crespo-Blanco, Patrick Winkert
semanticscholar +5 more sources
The Nehari manifold approach for singular equations involving the p(x)-Laplace operator [PDF]
Complex Variables and Elliptic Equations, 2021 We study the following singular problem involving the p$(x)$-Laplace operator $Δ_{p(x)}u= div(|\nabla u|^{p(x)-2}\nabla u)$, where $p(x)$ is a nonconstant continuous function, \begin{equation} \nonumber {(\rm P_λ)} \left\{\begin{aligned} - Δ_{p(x)} u & = a(x)|u|^{q(x)-2}u(x)+ \frac{λb(x)}{u^{δ(x)}} \quad\mbox{in}\,Ω,\\ u &>0 \quad\mbox{in ...
Dušan Repovš +2 more
semanticscholar +8 more sources
Existence and multiplicity for fractional Dirichlet problem with $γ(ξ)$-Laplacian equation and Nehari manifold [PDF]
arXiv, 2023 This paper is divided in two parts. In the first part, we prove coercivity results and minimization of the Euler energy functional. In the second part, we focus on the existence and multiplicity of a positive solution of fractional Dirichlet problem involving the $\gamma(\xi)$-Laplacian equation with non-negative weight functions in $\mathcal{H ...
Vanterler da C. Sousa +2 more
arxiv +5 more sources
The Nehari manifold for a degenerate logistic parabolic equation [PDF]
arXiv, 2023 The present paper analyses the behavior of solutions to a degenerate logistic equation with a nonlinear term of the form b(x)f(u), where the weight function b is assumed to be nonpositive. We exploit variational techniques and comparison principle in order to study the evolutionary dynamics.
Fernandes, Juliana, Maia, Liliane A.
arxiv +5 more sources
On the Nehari manifold for a logarithmic fractional Schrödinger equation with possibly vanishing potentials [PDF]
Mathematica Bohemica, 2022 We study a class of logarithmic fractional Schrödinger equations with possibly vanishing potentials. By using the fibrering maps and the Nehari manifold we obtain the existence of at least one nontrivial solution.
Cong Nhan Le, Xuan Truong Le
doaj +4 more sources
Nehari manifold optimization and its application for finding unstable solutions of semilinear elliptic PDEs [PDF]
arXivA Nehari manifold optimization method (NMOM) is introduced for finding 1-saddles, i.e., saddle points with the Morse index equal to one, of a generic nonlinear functional in Hilbert spaces. Actually, it is based on the variational characterization that 1-saddles of this functional are local minimizers of the same functional restricted on the associated
Zhaoxing Chen +3 more
arxiv +4 more sources
On branches of positive solutions for p-Laplacian problems at the extreme value of Nehari manifold method [PDF]
Proc. Amer. Math. Soc. 146 (2018), no. 7, 2925-2935, 2017 This paper is concerned with variational continuation of branches of solutions for nonlinear boundary value problems, which involve the p-Laplacian, the indefinite nonlinearity, and depend on the real parameter $\lambda$. A special focus is made on the extreme value of Nehari manifold $\lambda^*$, which determines the threshold of applicability of ...
Yavdat Il'yasov, Kaye Silva
arxiv +6 more sources