Results 1 to 10 of about 59 (54)
Monotonicity and Symmetry of Nonnegative Solutions to -Δ u=f(u) in Half-Planes and Strips. [PDF]
Adv Nonlinear Stud, 2017 We consider nonnegative solutions to -Δu=f(u)${-\Delta u=f(u)}$ in half-planes and strips, under zero Dirichlet boundary condition. Exploiting a rotating and sliding line technique, we prove symmetry and monotonicity properties of the solutions, under ...
Farina A, Sciunzi B.
europepmc +2 more sources
Advances in Nonlinear Analysis, 2023 We establish fine bounds for best constants of the fractional subcritical Sobolev embeddings W0s,p(Ω)↪Lq(Ω),{W}_{0}^{s,p}(\Omega )\hspace{0.33em}\hookrightarrow \hspace{0.33em}{L}^{q}(\Omega ), where N≥1N\ge 1 ...
Cassani Daniele, Du Lele
doaj +1 more source
Advances in Nonlinear Analysis, 2022 In this paper we study the existence and the nonexistence of solutions to an inhomogeneous non-linear elliptic problem (P)−Δu+u=F(u)+κμ in RN, u>0 in RN, u(x)→0 as |x|→∞,- \Delta u + u = F(u) + \kappa \mu \quad {\kern 1pt} {\rm in}{\kern 1pt ...
Ishige Kazuhiro +2 more
doaj +1 more source
Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction
Advances in Nonlinear Analysis, 2021 In the present paperwe study the existence of nontrivial solutions of a class of static coupled nonlinear fractional Hartree type system. First, we use the direct moving plane methods to establish the maximum principle(Decay at infinity and Narrow region
Wang Jun
doaj +1 more source
Advances in Nonlinear Analysis, 2021 We are concerned with a class of Choquard type equations with weighted potentials and Hardy–Littlewood–Sobolev lower critical ...
Zhou Shuai, Liu Zhisu, Zhang Jianjun
doaj +1 more source
Asymptotic properties of critical points for subcritical Trudinger-Moser functional
Advanced Nonlinear Studies, 2023 On a smooth bounded domain we study the Trudinger-Moser functional Eα(u)≔∫Ω(eαu2−1)dx,u∈H1(Ω){E}_{\alpha }\left(u):= \mathop{\int }\limits_{\Omega }({e}^{\alpha {u}^{2}}-1){\rm{d}}x,\hspace{1.0em}u\in {H}^{1}\left(\Omega ) for α∈(0,2π)\alpha \in \left(0 ...
Hashizume Masato
doaj +1 more source
Generic properties of the Rabinowitz unbounded continuum
Advanced Nonlinear Studies, 2023 In this article, we prove that, generically in the sense of domain variations, any solution to a nonlinear eigenvalue problem is either nondegenerate or the Crandall-Rabinowitz transversality condition that is satisfied. We then deduce that, generically,
Bartolucci Daniele +3 more
doaj +1 more source
Advances in Nonlinear Analysis, 2021 In this paper, we consider a class of semilinear elliptic equation with critical exponent and -1 growth. By using the critical point theory for nonsmooth functionals, two positive solutions are obtained. Moreover, the symmetry and monotonicity properties
Lei Chun-Yu, Liao Jia-Feng
doaj +1 more source
Multiple solutions to multi-critical Schrödinger equations
Advanced Nonlinear Studies, 2022 In this article, we investigate the existence of multiple positive solutions to the following multi-critical Schrödinger equation: (0.1)−Δu+λV(x)u=μ∣u∣p−2u+∑i=1k(∣x∣−(N−αi)∗∣u∣2i∗)∣u∣2i∗−2uinRN,u∈H1(RN),\left\{\begin{array}{l}-\Delta u+\lambda V\left(x)u=
Xu Ziyi, Yang Jianfu
doaj +1 more source
Advances in Nonlinear Analysis, 2021 In this paper we are concerned with the existence, nonexistence and bifurcation of nontrivial solution of the nonlinear Schrödinger-Korteweg-de Vries type system(NLS-NLS-KdV).
Geng Qiuping, Wang Jun, Yang Jing
doaj +1 more source