Results 31 to 40 of about 221 (69)
, 2017 In this paper we deal with the following fractional Kirchhoff equation \begin{equation*} \left(p+q(1-s) \iint_{\mathbb{R}^{2N}} \frac{|u(x)- u(y)|^{2}}{|x-y|^{N+2s}} \, dx\,dy \right)(-\Delta)^{s}u = g(u) \mbox{ in } \mathbb{R}^{N}, \end{equation*} where
Ambrosio, Vincenzo, Isernia, Teresa
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Semilinear problems for the fractional laplacian with a singular nonlinearity [PDF]
, 2015 The aim of this paper is to study the solvability of the problem (-Δ)s u = F(x,u) := λ f(x)/uγ + Mup in ω u > 0 in ω, u = 0 in RN \ ω, where Ω is a bounded smooth domain of RN, N > 2s, M ε {0, 1}, 0 0, λ > 0, p > 1 and f is a nonnegative function.
Barrios, B. +3 more
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, 2018 We obtain a new quantitative deformation lemma, and then gain a new mountain pass theorem. More precisely, the new mountain pass theorem is independent of the functional value on the boundary of the mountain, which improves the well known results (\cite ...
Ding, Liang +2 more
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Advances in Nonlinear AnalysisLet Ω⊂Rn\Omega \subset {{\bf{R}}}^{n} be a smooth bounded domain. In this article, we prove a result of which the following is a by-product: Let q∈]0,1[q\in ]0,1{[}, α∈L∞(Ω)\alpha \in {L}^{\infty }\left(\Omega ), with α>0\alpha \gt 0, and k∈Nk\in {\bf{N}}
Ricceri Biagio
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Variational Principles for Monotone and Maximal Bifunctions [PDF]
, 2003 2000 Mathematics Subject Classification: 49J40, 49J35, 58E30, 47H05We establish variational principles for monotone and maximal bifunctions of Brøndsted-Rockafellar type by using our characterization of bifunction’s maximality in reflexive Banach spaces.
Chbani, Zaki, Riahi, Hassan
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Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth
Advances in Nonlinear AnalysisWe study the following fractional Kirchhoff-Choquard equation: a+b∫RN(−Δ)s2u2dx(−Δ)su+V(x)u=(Iμ*F(u))f(u),x∈RN,u∈Hs(RN),\left\{\begin{array}{l}\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}{\left|{\left(-\Delta )}^{\frac{s}{2}}u\right|}
Yang Jie, Chen Haibo
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Advances in Nonlinear Analysis, 2017 The core of this paper concerns the existence (via regularity) of weak solutions in W01,2${W_{0}^{1,2}}$ of a class of elliptic systems such ...
Boccardo Lucio, Orsina Luigi
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Concentration-compactness at the mountain pass level in semilinear elliptic problems
, 2007 The concentration compactness framework for semilinear elliptic equations without compactness, set originally by P.-L.Lions for constrained minimization in the case of homogeneous nonlinearity, is extended here to the case of general nonlinearities in ...
TIntarev, Kyril
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Some remarks about the summability of nonlocal nonlinear problems
Advances in Nonlinear Analysis, 2015 In this note, we will study the problem (-Δ)psu = f(x) on Ω, u = 0 in ℝN∖Ω, where 0 < s < 1, (-Δ)ps is the nonlocal p-Laplacian defined below, Ω is a smooth bounded domain. The main point studied in this work is to prove, adapting the techniques used in [
Barrios Begoña +2 more
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On multiplicity of solutions to nonlinear Dirac equation with local super-quadratic growth
Advances in Nonlinear AnalysisIn this article, we study the following nonlinear Dirac equation: −iα⋅∇u+aβu+V(x)u=g(x,∣u∣)u,x∈R3.-i\alpha \hspace{0.33em}\cdot \hspace{0.33em}\nabla u+a\beta u+V\left(x)u=g\left(x,| u| )u,\hspace{1em}x\in {{\mathbb{R}}}^{3}.
Liao Fangfang, Chen Tiantian
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