Advanced Nonlinear Studies

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Maximal Regularity for Nonautonomous Evolution Equations
Advanced Nonlinear Studies - Tập 4 Số 4 - Trang 417-430 - 2004
Herbert Amann
Abstract We derive sufficient conditions, perturbation theorems in particular, for nonautonomous evolution equations to possess the property of maximal Lp regularity.
Asymptotic Nondegeneracy of Least Energy Solutions to an Elliptic Problem with Critical Sobolev Exponent
Advanced Nonlinear Studies - Tập 8 Số 4 - Trang 783-797 - 2008
Futoshi Takahashi
Abstract Consider the problem -∆u = N(N - 2)up + εk(x)u in Ω, u > 0 in Ω, u|∂Ω = 0 where Ω­ is a smooth bounded domain in ℝN (N ≥ 6), p = (N +2)/(N - 2), ε > 0 and k ∈ C2(Ω̅). Under certain assumptions, we prove the nondegeneracy of least energy solutions to the above problem as Ɛ →0. This is an extension of the recent work of Grossi [9].
Existence of Solutions for Some Classes of Singular Hamiltonian Systems
Advanced Nonlinear Studies - Tập 5 Số 2 - Trang 265-278 - 2005
Claudianor O. Alves, Francisco Júlio S.A. Corrêa, J. V. Gonçalves
Abstract This paper deals with existence of positive solution for the following singular Hamiltonian system where Ω ⊂ ℝN , N ≥ 2, is a smooth bounded domain and H, T, S, K are continuous functions. A key role is played by the Galerkin method.... hiện toàn bộ
Quasilinear Elliptic Equations on Half- and Quarter-spaces
Advanced Nonlinear Studies - Tập 13 Số 1 - Trang 115-136 - 2013
E. N. Dancer, Yihong Du, Messoud Efendiev
Abstract We consider quasilinear elliptic problems of the form Δpu + f(u) = 0 over the half-space H = {x ∈ ℝN : x1 > 0} and over the quarter-space Q = {x ∈ ℝN : x1 > 0, xN > 0}. In the half-space case we assume u ≥ 0 on ∂H, and in the quarter-space case we assume that u ≥ 0 on {x1 = 0} and u = 0 on {xN = 0}. Let u ≢ 0 be a bounded nonnegative solution. For some general classes of nonlinearities f ... hiện toàn bộ
Asymptotic Symmetry for a Class of Quasi-Linear Parabolic Problems
Advanced Nonlinear Studies - Tập 10 Số 4 - Trang 789-818 - 2010
Luigi Montoro, Berardino Sciunzi, Marco Squassina
Abstract We study the symmetry properties of the weak positive solutions to a class of quasi-linear elliptic problems having a variational structure. On this basis, the asymptotic behaviour of global solutions of the corresponding parabolic equations is also investigated. In particular, if the domain is a ball, the elements of the ω limit set are nonnegative radially symmetric solutions of the sta... hiện toàn bộ
Infinitely Many Nodal Solutions for Nonlinear Nonhomogeneous Robin Problems
Advanced Nonlinear Studies - Tập 16 Số 2 - Trang 287-299 - 2016
Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu
Abstract We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator which incorporates the p-Laplacian as special case. The reaction f ⁢ ( z , x ) ${f(z,x)}$ is a Carathéodory function which need not satisfy a global growth condition and is only assumed to be odd near zero. Using variational tools, we show that the problem has a whole sequence of distinct nodal (that is... hiện toàn bộ
On a Parametric Nonlinear Dirichlet Problem with Subdiffusive and Equidiffusive Reaction
Advanced Nonlinear Studies - Tập 14 Số 3 - Trang 565-591 - 2014
Nikolaos S. Papageorgiou, Patrick Winkert
Abstract We study a nonlinear parametric elliptic equation (nonlinear eigenvalue problem) driven by a nonhomogeneous differential operator. Our setting incorporates equations driven by the p-Laplacian, the (p, q)-Laplacian, and the generalized p-mean curvature differential operator. Applying variational methods we show that for λ > 0 (the parameter) sufficiently large the problem has at least thre... hiện toàn bộ
A General Approximation Approach for the Simultaneous Treatment of Integral and Discrete Operators
Advanced Nonlinear Studies - Tập 18 Số 4 - Trang 705-724 - 2018
Gianluca Vinti, Luca Zampogni
AbstractIn this paper, we give a unitary approach for the simultaneous study of the convergence of discrete and integral operators described by means of a family of linear continuous functionals acting on functions defined on locally compact Hausdorff topological groups. The general family of operators introduced and studied includes very well-known operators in the literature. We give results of ... hiện toàn bộ
Periodic Solutions of Equations of Emarkov-Pinney Type
Advanced Nonlinear Studies - Tập 6 Số 1 - Trang 57-67 - 2006
Meirong Zhang
Abstract After establishing a relation between the Hill’s equations and the Emarkov-Pinney equations, we are able to use degree theory to remove a technical assumption in [14], and give a complete set of non-resonance conditions for differential equations with repulsive singularities.
A Nonhomogeneous Fractional p-Kirchhoff Type Problem Involving Critical Exponent in ℝ N
Advanced Nonlinear Studies - Tập 17 Số 3 - Trang 611-640 - 2017
Mingqi Xiang, Binlin Zhang, Xia Zhang
Abstract This paper concerns itself with the nonexistence and multiplicity of solutions for the following fractional Kirchhoff-type problem involving the critical Sobolev exponent: [ a + b ⁢ ( ∬ ℝ 2 ⁢ N | u ⁢ ( x ) - u ⁢ ( y ) | p | x - y | N + p ⁢ s ⁢ 𝑑 x ⁢ 𝑑 y ) θ - 1 ] ⁢ ( - Δ ) p s ⁢ u = | u | p s * - 2 ⁢ u + λ ⁢ f ⁢ ( x )   in  ⁢ ℝ N , \Biggl{[}a+b\biggl{(}\iint_{\mathbb{R}^{2N}}\frac{\lver... hiện toàn bộ
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