We prove two multiplicity theorems producing two nodal solutions, and answer two open questions posed by Aizicovici et al. (2013) and by Barletta and Papageorgiou (2014). Our approach uses variational methods together with suitable truncation techniques and flow invariance arguments.doi:10.1016/j.nonrwa.2017.12.010He, TieshanGuo,...
Adimurthi&S. L. Yadava,Elementary proof of the non-existence of nodal solutions for the semilinear elliptic equations with critical Sobolev exponent, Nonlinear Anal.14(1990), 785–787. Google Scholar F. Atkinson, H. Brezis&L. A. Peletier,Solutions d'equations elliptiques avec exposant de Sobol...
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In this paper, we study the existence of least-energy nodal (sign-changing) solutions for a class of critical Schrödinger-Poisson system on the Heisenberg group given by {−ΔHu+μϕ|u|q−2u=λf(ξ,u)+|u|2u,inΩ,−ΔHϕ=|u|q,inΩ,u=ϕ=0,on∂Ω, whereΔHis the ...
Eq. (E) has infinitely many positive solutions belonging to H 1 (R N ). The above result (see also the subsequent [3] for a different proof and more general nonlinear- ities) is the starting point of our work; some comments and questions come naturally looking at ...
This reformulation only requires simple modifications to the original nodal force in both MPM and DDMP. After implementing this reformulated nodal force in a numerical code and comparing the results with manufactured solutions, we found significant improvements not only in the accuracy of the solutions...
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in this article because we were motivated by questions arising in the Ginzburg model of super-conductivity. Our results are also valid for the case of Dirichlet boundary conditions (see Remark 1.5 (vi)). Dirichlet boundary conditions are related to the Bohm-Aharonov effect for bounded states....
While proving Proposition 3.7 we have showed that one of the real contra-phasal solutions has the following values on the leads: ϕ (k) f1(k; x1) = cos 2 + kx1 f2(k; x2) = cos(γ(k))−1 sin(γ(k)) cos ϕ(k)−π 2 + kx2 0 γ (k) ∈/ 2πZ . γ (k) ...