[PDF] Top 20 On the existence of sign changing solutions for semilinear Dirichlet problems

... c) If 0 is a nondegenerate critical point with Morse index at least 2 and if is coercive then a simple argument using degree theory or the Morse inequalities yields the existence of four nontrivial critical ... See full document

... the existence of sign- changing solutions can be directly applied to problem ...the existence of sign-changing solution of such boundary-value ... See full document

... minimizer of on M may not be unique, and their arguments become invalid. This pa- per intends to address this problem caused by the dropping of this “strictly increasing” condition on f . Motivated by the works [2, 6, 9, ... See full document

... Here, by using critical point theory again, as well as Lyapunov-Schmidt reduction method and degree theory, a sharp condition to guarantee the existence of five or six solutions together with their ... See full document

... ecological problems, much attention has been attached to the existence of sign-changing solutions for nonlinear partial differential equations (see [–] and the references ...nonlocal ... See full document

... The rest of this paper is organized as follows. In Section , we give some lemmas which help to simplify the proofs of our main results. In Section , we discuss the existence and uniqueness of ... See full document

... Proof of Theorem 1.2 Since g(0) = 0, u(x) = 0 is a solution of (1.3). In this case, we are interested in finding the existence of sign-changing solutions to problem (1.3). The case g(t) = 0, ∀ ... See full document

... state solutions. In [], Huang et al. obtained the existence of at least a pair of fixed sign solutions and a pair of sign-changing solutions to system ...the ... See full document

... In recent years, many authors devoted to the study of (1.1) by employing var- ious methods and obtained some interesting results. Here we mention a few. Employing critical point theory, Agarwal [1] established the ... See full document

... the existence of a non- trivial solution of ...one sign changing ...the existence of sign changing solutions of ...of sign changing solutions u k (k ≥ ... See full document

... the existence of solutions or positive solutions of nonlinear ...of solutions for fractional differential equations; see [, , ...the existence of nontrivial sign-changing ... See full document

... and sign-changing weight function, which may not be integrable, we investigate the existence for the Dirichlet boundary value problems of strongly coupled vector p-Laplacian systems ... See full document

... longer a pointwise identical equation. This phenomenon provokes more difficulties to overcome, which makes the study of such a class of problems particularly interesting. If the function V vanishes and R N is ... See full document

... The existence of positive solutions for multi-point boundary value problems has been widely studied in recent ...the existence of n solutions and/or positive solutions to the ... See full document

... The theory of time scales was initiated by Hilger 1 as a mean of unifying and extending theories from differential and difference equations. The study of time scales has lead to several important applications in the study ... See full document

... This paper is organized as follows. In Sect. 2 we introduce Nehari manifold and state technical and elementary lemmas useful along the paper. In Sect. 3 we prove the existence of the first solution of (1.1). In ... See full document

... We also refer to a recent paper see 29 in which the proposition above was extended to the more general case of nonsmooth functionals. With the aid of Proposition 4.2, we can formulate the next lemma about the ... See full document

... for semilinear equations on the Heisenberg group have been studied by Birindelli et ...a semilinear Dirichlet problem involving critical nonlinearity on the half space of the Heisenberg ...other ... See full document

... the existence of nontrivial solutions for boundary value problems of the fol- lowing fourth order difference equation with a sign-changing ... See full document

... the existence of infinitely many solutions of P, under the assumption that V x is a function possibly changing sign in R N and fx, u also satisfies some growth ...change sign, which ... See full document