On the uniqueness of the positive solution of a singularly perturbed problem
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Publication:1912627
DOI10.1216/rmjm/1181072198zbMath0846.35046OpenAlexW2100409049MaRDI QIDQ1912627
Publication date: 29 September 1996
Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1216/rmjm/1181072198
Asymptotic behavior of solutions to PDEs (35B40) Nonlinear boundary value problems for linear elliptic equations (35J65) Singular perturbations in context of PDEs (35B25)
Related Items (27)
Further results on quasiperiodic partially localized solutions of homogeneous elliptic equations on \(\mathbb{R}^{N + 1} \) ⋮ Local uniqueness for the multi-bump solutions to the problem of Ambrosetti–Prodi type ⋮ Semilinear Neumann boundary value problems on a rectangle ⋮ Concentration on curves for a Neumann Ambrosetti-Prodi-type problem in two-dimensional domains ⋮ Unnamed Item ⋮ CONVERGENCE TO EQUILIBRIUM FOR SEMILINEAR PARABOLIC PROBLEMS IN ⋮ Elliptic equations with jumping nonlinearities involving high eigenvalues ⋮ Unnamed Item ⋮ Boundary concentrations on segments for a Neumann Ambrosetti-Prodi problem ⋮ Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods ⋮ The uniqueness of symmetric single peak solutions for a Neumann problem involving critical exponent. ⋮ Spectral asymptotics for nonlinear non-autonomous elliptic eigenvalue problems in a ball ⋮ Infinitely many positive solutions for nonlinear equations with non-symmetric potentials ⋮ Exact multiplicity for some nonlinear elliptic equations in balls ⋮ Uniqueness of positive solutions with concentration for the Schrödinger-Newton problem ⋮ On spikes concentrating on lines for a Neumann superlinear Ambrosetti-Prodi type problem ⋮ Concentration on submanifolds for an Ambrosetti-Prodi type problem ⋮ Multiple solutions for a class of elliptic equations with jumping nonlinearities ⋮ Existence and multiplicity of solutions for elliptic equations with jumping nonlinearities ⋮ On the existence of blowing-up solutions for a mean field equation ⋮ On the superlinear Lazer-McKenna conjecture ⋮ Exact multiplicity for some quasilinear elliptic Dirichlet problems where the non-linearity changes sign ⋮ Positive solutions for a nonlinear Schrödinger-Poisson system ⋮ Axial symmetry of some steady state solutions to nonlinear Schrödinger equations ⋮ Peak solutions without non-degeneracy conditions ⋮ The existence of partially localized periodic-quasiperiodic solutions and related KAM-type results for elliptic equations on the entire space ⋮ On the number of single-peak solutions of the nonlinear Schrödinger equation.
Cites Work
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