Multiple solutions for strongly resonant Robin problems
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201600454
Abstract: We consider nonlinear (driven by the p†Laplacian) and semilinear Robin problems with indefinite potential and strong resonance with respect to the principal eigenvalue. Using variational methods and critical groups, we prove four multiplicity theorems… read more here.
Keywords: robin; resonant robin; solutions strongly; multiple solutions ... See more keywords
Multiple Solutions for Nonvariational Quasilinear Elliptic Systems
Sign Up to like & getrecommendations! Published in 2018 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-018-1133-9
Abstract: We establish the existence of at least three nontrivial solutions for a nonvariational quasilinear elliptic system with homogeneous Dirichlet boundary condition. Two of these solutions are of opposite constant sign and the third one is… read more here.
Keywords: solutions nonvariational; nonvariational quasilinear; elliptic systems; multiple solutions ... See more keywords
Existence of Multiple Solutions of a Kirchhoff Type $p$-Laplacian Equation on the Sierpiński Gasket
Sign Up to like & getrecommendations! Published in 2019 at "Acta Applicandae Mathematicae"
DOI: 10.1007/s10440-019-00283-z
Abstract: In this paper, we study the following boundary value problem involving the weak $p$-Laplacian. $$ -M\bigl(\|u\|_{\mathcal{E}_{p}}^{p}\bigr)\Delta _{p} u = h(x,u) \quad \text{in}\ \mathcal{S}\setminus \mathcal{S}_{0}; \quad u = 0 \ \text{on}\ \mathcal{S}_{0}, $$ where $\mathcal{S}$ is… read more here.
Keywords: multiple solutions; kirchhoff type; existence multiple; solutions kirchhoff ... See more keywords
An Adaptive Orthogonal Basis Method for Computing Multiple Solutions of Differential Equations with Polynomial Nonlinearities
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-024-02557-7
Abstract: This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial nonlinearities. Departing from conventional practices of predefining candidate basis pools, our novel method… read more here.
Keywords: differential equations; basis; multiple solutions; polynomial nonlinearities ... See more keywords
Multiple Solutions of Boundary-Value Problems for Hamiltonian Systems
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-018-3847-4
Abstract: We consider two-point boundary-value problems for a Hamiltonian system of the form x′ = f(k, y), y′ = g(x, ????), where k and ???? are parameters. The numbers of solutions, both positive and oscillatory, for… read more here.
Keywords: problems hamiltonian; solutions boundary; boundary value; multiple solutions ... See more keywords
Existence of Multiple Solutions for a Class Non-uniformly Elliptic Equations with Critical Exponential Growth
Sign Up to like & getrecommendations! Published in 2018 at "Bulletin of the Iranian Mathematical Society"
DOI: 10.1007/s41980-018-0033-x
Abstract: This paper deals with the existence and multiplicity of weak solutions to non-uniformly elliptic problem $$\begin{aligned} -\text {div}(a(x,\nabla u))+V(x)\vert u\vert ^{N-2} u=\lambda \Bigg (\exp \Bigg (\alpha \vert u\vert ^{\frac{N}{N-1}}\Bigg )+f(x,u)\Bigg ), \end{aligned}$$-div(a(x,∇u))+V(x)|u|N-2u=λ(exp(α|u|NN-1)+f(x,u)),in $$\mathbb {R}^N$$RN, where… read more here.
Keywords: solutions class; vert; uniformly elliptic; multiple solutions ... See more keywords
Critical values in flow patterns of Magneto-Carreau fluid over a circular cylinder with diffusion species: Multiple solutions
Sign Up to like & getrecommendations! Published in 2017 at "Journal of The Taiwan Institute of Chemical Engineers"
DOI: 10.1016/j.jtice.2017.04.047
Abstract: Abstract Inspired by the various applications of non-Newtonian fluids, we carried out a numerical study for multiple solutions in MHD flow of Carreau viscosity model over a shrinking cylinder. This article is presumably the first… read more here.
Keywords: velocity; carreau fluid; cylinder; multiple solutions ... See more keywords
Ground state and multiple solutions for the fractional Schrödinger–Poisson system with critical Sobolev exponent
Sign Up to like & getrecommendations! Published in 2018 at "Nonlinear Analysis: Real World Applications"
DOI: 10.1016/j.nonrwa.2017.12.003
Abstract: Abstract In this paper, we study the following doubly singularly perturbed fractional Schrodinger–Poissonsystem with critical Sobolev exponent e 2 α ( − Δ ) α u + V ( x ) u + ϕ u… read more here.
Keywords: ground state; critical sobolev; multiple solutions; sobolev exponent ... See more keywords
Multiple solutions, oscillons and strange attractors in thermoviscoelastic marangoni convection
Sign Up to like & getrecommendations! Published in 2018 at "Physics of Fluids"
DOI: 10.1063/1.5040562
Abstract: Through numerical solution of the governing time-dependent and non-linear Navier-Stokes equations cast in the framework of the Oldroyd-B model, the supercritical states of thermal Marangoni-Benard convection in a viscoelastic fluid are investigated for increasing values… read more here.
Keywords: fluid; different branches; convection; time ... See more keywords
Does the fluid-static equilibrium of a self-gravitating isothermal sphere of van der Waals' gas present multiple solutions?
Sign Up to like & getrecommendations! Published in 2024 at "Physics of Fluids"
DOI: 10.1063/5.0248692
Abstract: We take up the investigation we left in the future-work stack in Giordano et al. [“Fluid statics of a self-gravitating isothermal sphere of van der Waals' gas,” Phys. Fluids 36, 056127 (2024)], in which we… read more here.
Keywords: van der; gas; multiple solutions; waals gas ... See more keywords
Multiple solutions to the static forward free–boundary Grad–Shafranov problem on MAST-U
Sign Up to like & getrecommendations! Published in 2025 at "Nuclear Fusion"
DOI: 10.1088/1741-4326/adf3cc
Abstract: The Grad–Shafranov (GS) equation is a nonlinear elliptic partial differential equation that governs the ideal magnetohydrodynamic equilibrium of a tokamak plasma. Previous studies have demonstrated the existence of multiple solutions to the GS equation when… read more here.
Keywords: static forward; grad shafranov; equilibrium; multiple solutions ... See more keywords