Herglotzův trik a rozklad kotangenty na parciální zlomky
Důkaz Brouwerovy věty metodou teorie grafů
Continuity of Nemyckij's operator in Hölder spaces
Nonlinear elliptic problems with jumping nonlinearities near the first eigenvalue
In this paper existence and multiplicity of solutions of the elliptic problem in on , are discussed provided the parameters and are close to the first eigenvalue . The sufficient conditions presented here are more general than those in given by S. Fučík in his aerlier paper.
Ranges of -homogeneous operators and their perturbations
Existence and multiplicity results for some weakly nonlinear elliptic problems at resonance
Jumping nonlinearities and mathematical models of suspension bridge
Solvability of the superlinear elliptic boundary value problem
Existence and multiplicity results for nonlinear noncoercive equations
Solvability of nonlinear problems at resonance
Bounded nonlinear perturbations of second order linear elliptic problems
Remarks on multiple periodic solutions of nonlinear ordinary differential equations
Remarks on nonlinear noncoercive problems with jumping nonlinearities
Positive solutions of some quasi-linear elliptic problems
Landesman-Lazer condition for periodic problems with jumping nonlinearities
A resonance problem for nonlinear Duffing equation
Landesman-Lazer type condition and nonlinearities with linear growth
Two notions which affected nonlinear analysis (Bernard Bolzano lecture)
General mathematical theories usually originate from the investigation of particular problems and notions which could not be handled by available tools and methods. The Fučík spectrum and the -Laplacian are typical examples in the field of nonlinear analysis. The systematic study of these notions during the last four decades led to several interesting and surprising results and revealed deep relationship between the linear and the nonlinear structures. This paper does not provide a complete survey....
The least eigenvalues of nonhomogeneous degenerated quasilinear eigenvalue problems
We prove the existence of the least positive eigenvalue with a corresponding nonnegative eigenfunction of the quasilinear eigenvalue problem where is a bounded domain, is a real number and , satisfy appropriate growth conditions. Moreover, the coefficient contains a degeneration or a singularity. We work in a suitable weighted Sobolev space and prove the boundedness of the eigenfunction in . The main tool is the investigation of the associated homogeneous eigenvalue problem and an application...
On Fredholm alternative for certain quasilinear boundary value problems
We study the Dirichlet boundary value problem for the -Laplacian of the form where is a bounded domain with smooth boundary , , , and is the first eigenvalue of . We study the geometry of the energy functional and show the difference between the case and the case . We also give the characterization of the right hand sides for which the above Dirichlet problem is solvable and has multiple solutions.
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