[PDF] Top 20 Infinitely Many Solutions for a Boundary Value Problem with Discontinuous Nonlinearities

... We explicitly observe that methods and techniques used in the proof of Theorem 3.1 can be applied to a wide class of nonlinear differential problems to investigate infinitely many solutions. The note ... See full document

... Our plan of the paper is as follows: in Section , we collect some well-known results to be used in the subsequent sections. In particular, we also present some new properties of Green’s function under the case M =  and ... See full document

... We study the existence of a class of nonlinear elliptic equation with Neumann boundary condition, and obtain infinitely many nodal solutions. The study of such a problem is based on the ... See full document

... Furthermore, the p-Laplacian often occurs in non-Newtonian fluid theory, nonlinear elastic mechanics, and so on. So, the impulsive fractional boundary value problem with p- Laplacian is worth ... See full document

... There are some common techniques to approach these problems: the fixed point theo- rems [, ], the method of upper and lower solutions [], or the topological degree theory [–]. On the other hand, in the last ... See full document

... positive solutions for higher order boundary value problems with integral boundary conditions on time ...order boundary value problem with integral boundary ... See full document

... in many areas, including fluid flow, electrical net- works, probability and statistics, chemical physics and signal processing and so on; see [–] and the references ...been many papers dealing with the ... See full document

... classical boundary value conditions have been considered in many papers, particularly in the second and fourth order cases, with either periodic or separated boundary conditions, see for ... See full document

... two solutions, exactly one solution and no solution, depending on the source term, when nonlinearities cross just the first ...three solutions, exactly one solution and no solution, depending on the ... See full document

... this, many authors have studied the existence of at least one solution, or multiple solutions, or even infinitely many solu- tions for fourth-order boundary value problems using ... See full document

... In critical point theory, Clark’s theorem [] asserts the existence of a sequence of neg- ative critical values tending to  for even coercive functionals. It is constantly and effec- tively applied to sublinear ... See full document

... in many literature sources, see ...to problem (P) has a mountain pass geometry but also to guarantee that the Palais-Smale sequence of the Euler-Lagrange functional is ... See full document

... of boundary value problems with continuous coefficients are highly developed, very little is known about a general char- acter of similar problems with ...years. Discontinuous boundary ... See full document

... Next, we prove our main results on the solvability of the problem (.), by applying the continuation theorem to the reference maps L + P and L + cI, where P denotes the orthog- onal projection onto the kernel of ... See full document

... example, many biological phenomena involving thresholds, bursting rhythm mod- els in medicine and biology, optimal control models in economics, and frequency mod- ulated systems, do exhibit impulsive ...multiple ... See full document

... fractional boundary conditions and obtained some new existence ...of solutions for the fractional nonlinear integro-differential equation of mixed type on a semi-infinite in- terval in a Banach ... See full document

... In the last number of years, it became evident that differential equations of non-integer order, also called fractionals (FDE’s), can capture better in models many of the relevant features of complex phenomena from ... See full document

... We deal with a perturbed eigenvalue Dirichlet-type problem for an elliptic hemivariational inequality involving the p-Laplacian. We show that an appropriate oscillating behaviour of the nonlinear part, even under ... See full document

... that problem (1.1) has infinitely many weak ...unbounded solutions) or at zero (for finding arbitrarily small solutions), while G, the primitive of g, has an appropriate growth (see ... See full document

... multiple solutions to the three-point boundary value problem u t atft, ut, u t 0, 0 < t < 1; u0 u 0 0; u 1 − αu η λ, where η ∈ 0, 1/2, α ∈ 1/2η, 1/η are constants, λ ∈ 0, ∞ is a ... See full document