Existence and multiplicity of solutions for fourth-order elliptic equations in \(\mathbb R^N\)

DOI10.1016/j.jmaa.2013.04.079zbMath1311.35094OpenAlexW1964289223MaRDI QIDQ2257571

Chun-Lei Tang, Yi-Wei Ye

Publication date: 25 February 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2013.04.079

zbMATH Keywords

mountain pass theoremcritical pointfourth-order elliptic equationsymmetric mountain pass theoremcerami sequences

Mathematics Subject Classification ID

Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Higher-order elliptic equations (35J30)

Related Items (38)

The existence of nontrivial solution for a class of sublinear biharmonic equations with steep potential well ⋮ Infinitely many solutions for a class of biharmonic equations with indefinite potentials ⋮ Existence of nontrivial solutions for a class of biharmonic equations with singular potential in \(\mathbb{R}^{N}\) ⋮ On a biharmonic equation with steep potential well and indefinite potential ⋮ Sign-changing solutions for fourth order elliptic equations with Kirchhoff-type ⋮ Existence and multiplicity of nontrivial solutions for some biharmonic equations with \(p\)-Laplacian ⋮ Ground states for a class of asymptotically linear fourth-order elliptic equations ⋮ Infinitely many sign-changing solutions for a class of biharmonic equation with \(p\)-Laplacian and Neumann boundary condition ⋮ Positive solutions for biharmonic equations: existence, uniqueness and multiplicity ⋮ Infinitely many high energy solutions for nonlocal fourth-order equation with sigh-changing potential ⋮ Positive solutions for a class of biharmonic problems: existence, nonexistence and multiplicity ⋮ Positive solutions for a class of biharmonic equations: existence and uniqueness ⋮ Ground-state solution for a class of biharmonic equations including critical exponent ⋮ Positive solutions of biharmonic elliptic problems with a parameter ⋮ Multiple solutions for generalized biharmonic equations with two singular terms ⋮ Infinitely many solutions for \(p\)-biharmonic equation with general potential and concave-convex nonlinearity in \(\mathbb{R}^{N}\) ⋮ Nodal ground state solution to a biharmonic equation via dual method ⋮ Multiple solutions for generalized biharmonic equations with singular potential and two parameters ⋮ Existence and concentration of a nonlinear biharmonic equation with sign-changing potentials and indefinite nonlinearity ⋮ Unnamed Item ⋮ Signed and sign-changing solutions of bi-nonlocal fourth order elliptic problem ⋮ Unnamed Item ⋮ High energy solutions for the fourth-order elliptic equations in \(\mathbb R^N\) ⋮ Solutions of biharmonic equations with mixed nonlinearity ⋮ Least energy nodal solution for quasilinear biharmonic equations with critical exponent in \(\mathbb{R}^N\) ⋮ Nontrivial solutions and least energy nodal solutions for a class of fourth-order elliptic equations ⋮ Existence of multi-bump solutions for a class of elliptic problems involving the biharmonic operator ⋮ High energy solutions of modified quasilinear fourth-order elliptic equations with sign-changing potential ⋮ Fourth-order nonlocal type elliptic problems with indefinite nonlinearities ⋮ Multiplicity and concentration of nontrivial solutions for the generalized extensible beam equations ⋮ Unnamed Item ⋮ Least energy sign-changing solutions for fourth-order Kirchhoff-type equation with potential vanishing at infinity ⋮ Infinitely many solutions for fourth-order semilinear \(\Delta_{\gamma}\)-Laplace equation in \(\mathbb{R}^N\) ⋮ Multiplicity of solutions for fourth-order elliptic equations with p-Laplacian and mixed nonlinearity ⋮ Adams' type inequality and application to a quasilinear nonhomogeneous equation with singular and vanishing radial potentials in \( \mathbb{R}^4 \) ⋮ Sign-changing solutions for Schrödinger-Kirchhoff-type fourth-order equation with potential vanishing at infinity ⋮ GROUND STATE AND NODAL SOLUTIONS FOR A CLASS OF BIHARMONIC EQUATIONS WITH SINGULAR POTENTIALS ⋮ Radial and non-radial multiple solutions to a general mixed dispersion NLS equation

Cites Work

• Unnamed Item
• Unnamed Item
• A note on nonlinear fourth-order elliptic equations on \(\mathbb R ^N\)
• Existence and concentration of solutions for a class of biharmonic equations
• Infinitely many solutions for fourth-order elliptic equations
• Existence and multiplicity of solutions for a class of fourth-order elliptic equations in \(R^N\)
• High energy solutions and nontrivial solutions for fourth-order elliptic equations
• Multiplicity results for some fourth-order elliptic equations
• Infinitely many nontrivial solutions for a class of biharmonic equations via variant Fountain theorems
• Fourth-order Navier boundary value problem with combined nonlinearities
• Multiple nontrivial solutions for some fourth-order semilinear elliptic problems
• Bound states for semilinear Schrödinger equations with sign-changing potential
• Multiple and sign-changing solutions for a class of semilinear biharmonic equation
• Infinitely many sign-changing solutions for a class of biharmonic equation without symmetry
• Global bifurcation and a theorem of Tarantello
• Traveling waves in a nonlinearly suspended beam: Theoretical results and numerical observations
• On some fourth-order semilinear elliptic problems in \(\mathbb R^N\)
• Multiple solutions for a class of nonlinear Schrödinger equations
• Sign-changing solutions for some fourth-order nonlinear elliptic problems
• A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations
• Sign-changing critical points from linking type theorems
• Travelling Waves in a Suspension Bridge
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• Radial Entire Solutions of Even Order Semilinear Elliptic Equations
• Critical semilinear biharmonic equations in R^N
• Nontrivial solutions for some fourth order semilinear elliptic problems
• Multiplicity results for a fourth-order semilinear elliptic problem
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis

This page was built for publication: Existence and multiplicity of solutions for fourth-order elliptic equations in \(\mathbb R^N\)