caa a22 4500 445830689 CHVBK 20180317145314.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10255-011-0076-8 doi (NATIONALLICENCE)springer-10.1007/s10255-011-0076-8 Existence of positive solutions for a general nonlinear eigenvalue problem [Elektronische Daten] [Xi-you Cheng, Zhi-tao Zhang] Let Ω ⊂ ℝn be a bounded domain, H = L 2(Ω), L: D(L) ⊂ H → H be an unbounded linear operator, f ∈ C($\bar \Omega$ × ℝ, ℝ) and λ ∈ ℝ. The paper is concerned with the existence of positive solutions for the following nonlinear eigenvalue problem $Lu = \lambda f\left( {x,u} \right), u \in D\left( L \right),$ which is the general form of nonlinear eigenvalue problems for differential equations. We obtain the global structure of positive solutions, then we apply the results to some nonlinear eigenvalue problems for a secondorder ordinary differential equation and a fourth-order beam equation, respectively. The discussion is based on the fixed point index theory in cones. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg, 2011 unbounded linear operator nationallicence fixed point index nationallicence positive solution nationallicence Cheng Xi-you Academy of Mathematics and Systems Science, Institute of Mathematics, Chinese Academy of Sciences, 100190, Beijing, China aut Zhang Zhi-tao Academy of Mathematics and Systems Science, Institute of Mathematics, Chinese Academy of Sciences, 100190, Beijing, China aut Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/3(2011-07-01), 367-372 0168-9673 27:3<367 2011 27 10255 https://doi.org/10.1007/s10255-011-0076-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10255-011-0076-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cheng Xi-you Academy of Mathematics and Systems Science, Institute of Mathematics, Chinese Academy of Sciences, 100190, Beijing, China aut NATIONALLICENCE 700 1- Zhang Zhi-tao Academy of Mathematics and Systems Science, Institute of Mathematics, Chinese Academy of Sciences, 100190, Beijing, China aut NATIONALLICENCE 773 0- Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/3(2011-07-01), 367-372 0168-9673 27:3<367 2011 27 10255 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer