On the Superlinear Lazer–McKenna Conjecture: Part II

DOI10.1080/03605300500258865zbMath1330.35147OpenAlexW2036314248MaRDI QIDQ5708013

Shusen Yan, E. Norman Dancer

Publication date: 25 November 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300500258865

zbMATH Keywords

variational methodspeak solutionsfinite dimensional reductions

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) Perturbations of nonlinear operators (47H14)

Related Items (23)

Local uniqueness for the multi-bump solutions to the problem of Ambrosetti–Prodi type ⋮ Boundary bubbling solutions for a planar elliptic problem with exponential Neumann data ⋮ Concentration on curves for a Neumann Ambrosetti-Prodi-type problem in two-dimensional domains ⋮ On the fractional Lazer-McKenna conjecture with superlinear potential ⋮ Bubbling solutions for an anisotropic planar elliptic problem with exponential nonlinearity ⋮ Elliptic equations with jumping nonlinearities involving high eigenvalues ⋮ On the Hollman McKenna conjecture: interior concentration near curves ⋮ The two-dimensional Lazer-McKenna conjecture for an exponential nonlinearity ⋮ Boundary concentrations on segments for a Neumann Ambrosetti-Prodi problem ⋮ Exact number of single bubbling solutions for elliptic problems of Ambrosetti-Prodi type ⋮ Lazer-McKenna conjecture: the critical case ⋮ Relative equilibria in continuous stellar dynamics ⋮ On the fractional Lazer-McKenna conjecture with critical growth ⋮ The Lazer-McKenna conjecture for an anisotropic planar elliptic problem with exponential Neumann data ⋮ Multiple peak solutions for polyharmonic equation with critical growth ⋮ Lazer-McKenna conjecture for fractional problems involving critical growth ⋮ The critical Lazer-McKenna conjecture in low dimensions ⋮ On spikes concentrating on lines for a Neumann superlinear Ambrosetti-Prodi type problem ⋮ Nonradial solutions of a nonhomogeneous semilinear elliptic problem with linear growth ⋮ Concentration on submanifolds for an Ambrosetti-Prodi type problem ⋮ The Lazer-McKenna conjecture for an elliptic problem with critical growth. II ⋮ Multiplicity of solutions for a superlinear \(p\)-Laplacian equation ⋮ Lazer-McKenna conjecture for higher order elliptic problem with critical growth

Cites Work

• Multiplicity results for superlinear elliptic problems with partial interference with the spectrum
• A symmetry theorem and applications to nonlinear partial differential equations
• Variational and topological methods in partially ordered Hilbert spaces
• On the number of solutions of a nonlinear Dirichlet problem
• Asymptotic shape and location of small cores in elliptic free-boundary problems
• Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof.
• On the superlinear Lazer-McKenna conjecture
• On the inversion of some differentiable mappings with singularities between Banach spaces
• Dual variational methods in critical point theory and applications
• A counterexample to the Lazer–McKenna conjecture
• On the superlinear Ambrosetti-Prodi problem
• On a conjecture related to the number of solutions of a nonlinear Dirichlet problem
• A Variational approach to superlinear elliptic problems
• Multiplicity results for Ode's with nonlinearities crossing all but a finite number of eigenvalues
• On a Class of Superlinear Sturm–Liouville Problems with Arbitrarily Many Solutions

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