Results 11 to 20 of about 475 (219)
Choquard equations via nonlinear rayleigh quotient for concave-convex nonlinearities
Communications on Pure and Applied Analysis, 2021 It is established existence of ground and bound state solutions for Choquard equation considering concave-convex nonlinearities in the following form $$ \begin{array}{rcl} -Δu +V(x) u &=& (I_α* |u|^p)|u|^{p-2}u+ λ|u|^{q-2}u, \, u \in H^1(\mathbb{R}^{N}), \end{array} $$ where $λ> 0, N \geq 3, α\in (0, N)$.
Carvalho, M. L. M. +2 more
openaire +4 more sources
Fractal and Fractional, 2022 In this paper, we use the fixed-point index to establish positive solutions for a system of Riemann–Liouville type fractional-order integral boundary value problems.
Keyu Zhang +3 more
doaj +1 more source
Radial solutions of Dirichlet problems with concave–convex nonlinearities [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2011 The authors consider the nonlinear Dirichlet problem \[ \begin{gathered} \Delta u(x)+ q(|x|)|u(x)|^{\delta-1} u(x)+ p(|x|)|u(x)|^{\gamma-1} u(x)= 0,\quad x\in\Omega,\\ u(x)= 0,\qquad x\in\partial\Omega,\end{gathered}\tag{1} \] where \(\Omega\) is the unit ball in \(\mathbb{R}^N\) with \(N\geq 3\) and \(p,q:[0,1]\to \mathbb{R}\) are \(C^1\)-functions; \(
DALBONO, Francesca, Dambrosio W.
openaire +1 more source
Extremal parameter for double phase problem with concave–convex nonlinearity
Communications in Nonlinear Science and Numerical Simulation, 2023 Abstract Note: Please see pdf for full abstract with equations. In this work, we study the following problem −Δpu − div(μ(x)|∇u|q−2∇u) = λf(x)|u|γ−2u + g(x)|u|r−2u in Ω, u = 0 on ∂Ω, where Ω ⊂ RN,N ≥ max{2, p} is a bounded smooth domain, 1 < γ < p < q
P. K. Mishra +2 more
openaire +2 more sources
Multiplicity of Solutions for Schrödinger Equations with Concave-Convex Nonlinearities [PDF]
International Journal of Analysis, 2016 We study the multiplicity of solutions for a class of semilinear Schrödinger equations: -Δu+V(x)u=gx,u, for x∈RN; u(x)→0, as u→∞, where V satisfies some kind of coercive condition and g involves concave-convex nonlinearities with indefinite signs. Our theorems contain some new nonlinearities.
Dong-Lun Wu, Chun-Lei Tang, Xing-Ping Wu
openaire +2 more sources
Boundary Value Problems, 2023 In this paper, we study the existence of a class of p ( x ) $p(x)$ -Kirchhoff equation involving concave-convex nonlinearities. The main tools used are the perturbation technique, variational method, and a priori estimation.
Changmu Chu, Zhongju He
doaj +1 more source
The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent [PDF]
Sahand Communications in Mathematical Analysis, 2018 In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains.
Somayeh Khademloo, Saeed Khanjany Ghazi
doaj +1 more source
A class of fourth-order elliptic equations with concave and convex nonlinearities in $\mathbb{R}^N$
Electronic Journal of Qualitative Theory of Differential Equations, 2021 In this article, we study the multiplicity of solutions for a class of fourth-order elliptic equations with concave and convex nonlinearities in $\mathbb{R}^N$.
Zijian Wu, Haibo Chen
doaj +1 more source
On Multiple Solutions of Concave and Convex Nonlinearities in Elliptic Equation on ℝN
Boundary Value Problems, 2009 We consider the existence of multiple solutions of the elliptic equation on ℝN with concave and convex nonlinearities.
Kuan-Ju Chen
doaj +1 more source
MULTIPLICITY OF SOLUTIONS FOR DOUBLE PHASE EQUATIONS WITH CONCAVE-CONVEX NONLINEARITIES
Journal of Applied Analysis & Computation, 2021 Summary: This paper is devoted to the study of the \(L^\infty \)-bound of solutions to a double-phase problem with concave-convex nonlinearities by applying the De Giorgi's iteration method and the localization method. Employing this and a variant of Ekeland's variational principle, we provide the existence of at least two distinct nontrivial solutions
Joe, Woo Jin +3 more
openaire +2 more sources