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  • 1. Jalilian, Yaghoub
    et al.
    Szulkin, Andrzej
    Stockholm University, Faculty of Science, Department of Mathematics.
    Infinitely many solutions for semilinear elliptic problems with sign-changing weight functions:  2014In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, no 4, p. 756-770Article in journal (Refereed)
    Abstract [en]

    In this paper we study the elliptic problem\begin{equation*} \left\{\begin{array}{ll} -\Delta u+u = a(x)|u|^{p-2}u+b(x)|u|^{q-2}u,\\ u\in H^{1}(\mathbb{R}^{N}),\end{array}\right.\end{equation*}where $2^{*}$ is the critical Sobolev exponent, $2< p<q< 2^{*}$and $a$ or $b$ is a sign-changing function. Under different assumptions on $a$ and $b$ we prove the existenceof infinitely many solutions to the above problem. We also show that one of these solutions is positive.

  • 2. Martynuk, Olga
    et al.
    Pivovarchik, Vyacheslav
    Tretter, Christiane
    Stockholm University, Faculty of Science, Department of Mathematics. Universität Bern, Switzerland.
    Inverse problem for a damped Stieltjes string from parts of spectra2015In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 94, no 12, p. 2605-2619Article in journal (Refereed)
    Abstract [en]

    We solve the following inverse problem for boundary value problems generated by the difference equations describing the motion of a Stieltjes string (a thread with beads). Given are certain parts of the spectra of two boundary value problems with two different Robin conditions at the left end and the same damping condition at the right end. From these two partial spectra, the difference of the Robin parameters, the damping constant, and the total length of the string, find the values of the point masses, and of the lengths of the intervals between them. We establish necessary and sufficient conditions for two sets of complex numbers to be the eigenvalues of two such boundary value problems and give a constructive solution of the inverse problem.

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