Page 1 Lecture Notes in Mathematics Filippo Gazzola Hans-Christoph Grunau Guido Sweers
Polyharmonic Boundary Value Problems 1991 Positivity Preserving and Nonlinear Higher …

We prove existence of nontrivial solutions to semilinear fourth order problems at critical
growth in some contractible domains which are perturbations of small capacity of domains …

We prove a Sobolev inequality with remainder term for the imbedding D^m,2(R^N) ↪
L^2N/(N-2m)(R^N), m∈N arbitrary, generalizing a corresponding result of Bianchi and …

On some fourth-order semilinear elliptic problems in RN - ScienceDirect Skip to main
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Existence and multiplicity of solutions for a fourth-order elliptic equation | Boundary Value
Problems Skip to main content SpringerLink Account Menu Find a journal Publish with us …

We establish the existence of multiple solutions to the Dirichlet problem for the equation -
Δu=λu+|u|^4N-2u on a bounded domain Ω of R^N, N\geq4. We show that, if λ>0 is not a …

The entire positive solutions of a conformally invariant biharmonic equation in Rn will be
classified using the method of moving spheres. As a byproduct, one also shows that any …

Using variational methods, we obtain several multiplicity results for double phase problems
that involve variable exponents and a new type of critical growth. This new critical growth is …

Gilbarg and Trudinger [1, Corollary 9.10], and the Hilbert space H2 (Ω)∩ H1 0 (Ω) can be
endowed with the scalar product (u, v)=∫ Ω∆ u∆ vdx, which induces the norm u=∆ uL2 (Ω) …

By a variant version of Fountain Theorem due to Zou [W. Zou, Variant fountain theorems and
their applications, Manuscripta Math. 104 (2001) 343–358], the existence of infinitely many …