Positive solution and bifurcation from the essential spectrum of a semilinear elliptic equation on Rn

DOI10.1016/0362-546X(90)90152-7zbMath0729.35049OpenAlexW1985903064MaRDI QIDQ3353435

Dao-Min Cao

Publication date: 1990

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(90)90152-7

zbMATH Keywords

positive solutionsemilinear elliptic equationbifurcation from the essential spectrum

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Bifurcations in context of PDEs (35B32) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

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Non-degeneracy and existence of new solutions for the Schrödinger equations ⋮ Infinitely many positive solutions for the nonlinear Schrödinger equations in \(\mathbb R^N\) ⋮ Semilinear elliptic problems with singular potentials in ℝ^N ⋮ The existence of positive solutions for the Neumann problem of \(p\)-Laplacian elliptic systems with Sobolev critical exponent ⋮ High energy solutions of the Choquard equation ⋮ Unnamed Item ⋮ Multiplicity of positive and nodal solutions for nonlinear elliptic problems in \(\mathbb{R}^ N\) ⋮ Positive solutions with high energy for fractional Schrödinger equations ⋮ Solutions of Schrödinger equations with inverse square potential and critical nonlinearity ⋮ A global compactness result with applications to a nonlinear elliptic equation arising in astrophysics ⋮ Existence of multiple positive solutions for nonhomogeneous elliptic problems in \(\mathbb R^{N}\) ⋮ Existence of entire positive solutions for nonhomogeneous elliptic equations ⋮ Multiplicity of 2-nodal solutions for semilinear elliptic problems in \(\mathbb R^N\) ⋮ Existence and multiplicity of positive solutions for Dirichlet problems in unbounded domains ⋮ Infinitely many positive solutions of fractional nonlinear Schrödinger equations with non-symmetric potentials ⋮ The existence of multiple positive solutions for a semilinear elliptic equation in \(\mathbb R^N\) ⋮ Multiple existence of sign changing solutions for semilinear elliptic problems on \(\mathbb{R}^N\) ⋮ Infinitely many positive solutions for a nonlinear field equation with super-critical growth ⋮ INFINITELY MANY POSITIVE SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER–POISSON SYSTEM ⋮ Large energy bubble solutions for Schrödinger equation with supercritical growth ⋮ Existence of solutions for some fourth-order nonlinear elliptic problems ⋮ Multiplicity of positive and nodal solutions for nonlinear elliptic problems in R^N ⋮ Intermediate reduction method and infinitely many positive solutions of nonlinear Schrödinger equations with non-symmetric potentials ⋮ Infinitely many non-radial positive solutions to the double-power nonlinear Schrödinger equations ⋮ Solutions with multiple peaks for nonlinear elliptic equations ⋮ SINGULAR ELLIPTIC PROBLEMS WITH CRITICAL GROWTH

Cites Work

• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Positive solutions of some nonlinear elliptic problems in exterior domains
• On the existence of positive entire solutions of a semilinear elliptic equation
• Uniqueness of solutions of semilinear Poisson equations
• Unnamed Item
• Unnamed Item
• Unnamed Item

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