This paper proves that any nonregular nonparametric saddle surface in a three-dimensional space of nonzero constant curvature $k$, which is bounded by a rectifiable curve, is a space of curvature not greater than $k$ in the sense of Aleksandrov. This generalizes a classical theorem by Shefel′ on saddle surfaces in ${𝔼}^3$.

By means of Morse theory we prove the existence of a nontrivial solution to a superlinear $p$-harmonic elliptic problem with Navier boundary conditions having a linking structure around the origin. Moreover, in case of both resonance near zero and nonresonance at $+\infty$ the existence of two nontrivial solutions is shown.

The integral wavelet transform is defined in weighted Sobolev spaces, in which some properties of the transform as well as its asymptotical behaviour for small dilation parameter are studied.

We study minimal solutions for one-dimensional variational problems on a torus. We show that, for a generic integrand and any rational number $\alpha$, there exists a unique (up to translations) periodic minimal solution with rotation number $\alpha$.

This work is devoted to the study of a quasilinear elliptic system of resonant type. We prove the existence of infinitely many solutions of a related nonlinear eigenvalue problem. Applying an abstract minimax theorem, we obtain a solution of the quasilinear system $-{\Delta }_{p}u=F_u\left(x,u,v\right),-{\Delta }_{q}v=F_v\left(x,u,v\right)$, under conditions involving the first and the second eigenvalues.