Existence of solutions for higher order BVP with parameters via critical point theory

• Autorzy: Jurkiewicz M. , Przeradzki B.
• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with the existence of at least one solution of the nonlinear 2k-th order BVP. We use the Mountain Pass Lemma to get an existence result for the problem, whose linear part depends on several parameters.

Słowa kluczowe

EN

multidimensional spectrum; Lidstone BVP; critical point theory; Palais-Smale condition

PL

widma wielowymiarowe; teoria punktu krytycznego; warunek Palais-Smale'a

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2015
• Tom: Vol. 48, nr 1
• Strony: 53--61
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Jurkiewicz M.

• Institute of Mathematics and Cryptology, Military University of Technology, Gen. Sylwestra Kaliskiego 2, 00-908 Warszawa 49, Poland

autor

Przeradzki B.

• Institute of Mathematics, Lodz University of Technology, Wólczańska 215, 90-924 Łódź, Poland

Bibliografia

• [1] R. P. Agarwal, D. O’Regan, S. Staněk, Singular Lidstone boundary value problem with given maximal values for solutions, Nonlinear Anal. 55 (2003), 859–881.
• [2] O. Bratteli, D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 1, Springer-Verlag, Berlin, Heidelberg, 1987.
• [3] M. Jurkiewicz, On solutions of fourth-order Lidstone boundary value problem at resonance , Ann. Polon. Math. 95 (2009), 1–16.
• [4] M. Jurkiewicz, Existence result for the Lidstone boundary value problem at resonance, J. Math. Anal. Appl. 394 (2012), 248–259.
• [5] M. Jurkiewicz, Some remarks on exact solution of Lidstone boundary value problem, Biuletyn WAT 61 (2012), 343–358.
• [6] M. Jurkiewicz, Existence of infinitely many solutions to Lidstone BVP, (submitted).
• [7] Y. Li, Positive solutions of fourth-order boundary value problems with two parameters, J. Math. Anal. Appl. 281 (2003), 477–484.
• [8] M. Struwe, Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, 4th Ed., Springer-Verlag, Berlin, Heidelberg, 2008.
• [9] Y.-M. Wang, On 2nth-order Lidstone boundary value problems, J. Math. Anal. Appl. 312 (2005), 383–400.