Fractional double phase Robin problem involving variable order-exponents without Ambrosetti–Rabinowitz condition

نویسندگان

چکیده

We consider a fractional double phase Robin problem involving variable order and exponents. The nonlinearity $f$ is Carath\'{e}odory function satisfying some hypotheses which do not include the Ambrosetti-Rabinowitz type condition. By using Variational methods, we investigate multiplicity of solutions.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Traces for Fractional Sobolev Spaces with Variable Exponents

In this note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if p : Ω × Ω → (1,∞) and q : ∂Ω→ (1,∞) are continuous functions such that (n− 1)p(x, x) n− sp(x, x) > q(x) in ∂Ω ∩ {x ∈ Ω: n− sp(x, x) > 0}, then the inequality ‖f‖Lq(·)(∂Ω) ≤ C { ‖f‖Lp̄(·)(Ω) + [f ]s,p(·,·) } holds. Here p̄(x) = p(x, x) and [f ]s,p(·,·) denotes the fractional semi...

متن کامل

Radial Solutions to a Dirichlet Problem Involving Critical Exponents

In this paper we show that, for each λ > 0, the set of radially symmetric solutions to the boundary value problem −∆u(x) = λu(x) + u(x)|u(x)|, x ∈ B := {x ∈ R : ‖x‖ < 1}, u(x) = 0, x ∈ ∂B, is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.

متن کامل

A nonlinear general Neumann problem involving two critical exponents

We discuss the existence of solutions to the following nonlinear problem involving two critical Sobolev exponents  −div(p(x)∇u) = β|u|2−2u+ f(x, u) in Ω, u 6≡ 0 in Ω, ∂u ∂ν = Q(x)|u| 2∗−2u on ∂Ω, where β ≥ 0, Q is continuous on ∂Ω, p ∈ H(Ω) is continuous and positive in Ω̄ and f is a lower-order perturbation of |u|2−1 with f(x, 0) = 0.

متن کامل

Radially Symmetric Solutions to a Dirichlet Problem Involving Critical Exponents

In this paper we answer, for N = 3, 4, the question raised in [1] on the number of radially symmetric solutions to the boundary value problem -Au(x) = Xu(x) + u(x)\u(x)\4/(-N-2'i, x G B := {x e RN: \\x\\ < 1}, u(x) = 0 , x e dB , where A is the Laplacean operator and X > 0 . Indeed, we prove that if N = 3, 4 , then for any A > 0 this problem has only finitely many radial solutions. For N = 3, 4...

متن کامل

MIXED BOUNDARY VALUE PROBLEM FOR A QUARTER-PLANE WITH A ROBIN CONDITION

We consider a mixed boundary value problem for a quarter-plane with a Robin condition on one edge. We have developed two procedures, one based on the advanced theory of dual integral equations and the other, in our opinion simpler technique, relying on conformal mapping. Both of the procedures are of interest, because the former may be easier to adapt to other boundary value problems.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Zeitschrift für Angewandte Mathematik und Physik

سال: 2022

ISSN: ['1420-9039', '0044-2275']

DOI: https://doi.org/10.1007/s00033-022-01724-w