Search

This article concerns the existence and multiplicity of solutions for the singular p-biharmonic problem involving the Hardy potential and the critical Hardy-Sobolev exponent. To this end we use variational methods combined with the Mountain pass theorem and the Ekeland variational principle. We illustrate the usefulness of our results with and example. [ABSTRACT FROM AUTHOR]

We study the fractional p-Kirchhoff equation ... where (-∆)s2 is the fractional p-Laplacian operator, a and b are strictly positive real numbers, s ∈ (0, 1), 1 < p < N/s, and p < q < p*s - 2 with p*s = Np/N-ps. By using the variational method, we prove the existence and uniqueness of global minimum or mountain pass type critical points on the Lp-normalized manifold S(c):= {u∈ 2 Ws,p(RN): RRN = cp. [ABSTRACT FROM AUTHOR]

We consider a Brezis-Nirenberg problem on the hyperbolic space Hn. By using the stereographic projection, the problem becomes a singular problem on the boundary of the open ball B1(0) ⊂ Rn. Thanks to the Hardy inequality, in a version due to Brezis-Marcus, the difficulty involving singularities can be overcame. We use the mountain pass theorem due to Ambrosetti-Rabinowitz and Brezis-Nirenberg arguments to obtain a nontrivial solution. [ABSTRACT FROM AUTHOR]

In this article, we prove the existence of solutions for some discrete nonlinear difference equations subjected to a potential boundary type condition. We use a variational technique that relies on Szulkin's critical point theory, which ensures the existence of solutions by ground state and mountain pass methods. [ABSTRACT FROM AUTHOR]

This article concerns the nonhomogeneous Klein-Gordon-Maxwell equation -Δu + u - (2w + Φ) Φu + |u|p-1u + h(x), in ℝ³; ΔΦ = (w + Φ)u², in ℝ³, where w > 0 is constant, p ∈ (1; 5). Under appropriate assumptions on h(x), the existence of at least two solutions is obtained by applying the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. [ABSTRACT FROM AUTHOR]

This article concerns the existence of solutions to boundary-value problems involving the p(x)-biharmonic operator. Our technical approach is the variational-hemivariational inequality on bounded domains by using the mountain pass theorem and the critical point theory for Motreanu-Panagiotopoulos type functionals. [ABSTRACT FROM AUTHOR]