1,721,099 research outputs found
BMO REGULARITY FOR ASYMPTOTIC PARABOLIC SYSTEMS WITH LINEAR GROWTH
No full textWe prove local regularity results for the spatial gradient of weak solutions to nonlinear problems under the assumption that the involved operator becomes appropriately parabolic at infinity
Sign-changing solutions for a fractional Kirchhoff equation
Full text linkUsing a minimization argument and a quantitative deformation lemma, we establish the existence of least energy sign-changing solutions for the following nonlinear Kirchhoff problem (a+b[u]2)(−Δ)su+V(x)u=K(x)f(u)inR3,where a,b>0 are constants, s∈(0,1), (−Δ)s is the fractional Laplacian, V,K are continuous, positive functions, allowed for vanishing behavior at infinity, and f is a continuous function satisfying suitable growth assumptions. Moreover, when the nonlinearity f is odd, we obtain the existence of infinitely many nontrivial weak solutions not necessarily nodals
On a nonhomogeneous sublinear-superlinear fractional equation in RN
No full textThe existence of a positive solution to a nonhomogeneous fractional sublinear-superlinear problem in the whole space is proved by combining a minimization method, Nehari manifold and the fibering map methods, and the concentration-compactness lemma. We also study the continuity of solutions in the perturbation parameter f at 0
Nonhomogeneous sublinear fractional Schrödinger equations
No full textWe study the existence, uniqueness and multiplicity for the sublinear fractional problem (−∆)su + V (x)u + a(x)|u|p sgn(u) = f in RN, where s ∈ (0, 1), N > 2s, (−∆)s is the fractional Laplacian, p ∈ (0, 1), f ∈ L2(RN ) ∩ Lp+1/p (RN ), V: RN → R and a: RN → R are positive bounded functions
Positive solution for nonhomogeneous sublinear fractional equations in
No full textUsing a minimization argument on the Nehari manifold, we prove that the following sublinear fractional problem (Formula presented.) possesses a unique positive weak solution provided that (Formula presented.) and (Formula presented.). Moreover, this solution converges to zero in (Formula presented.) when (Formula presented.) tends to zero
-regularity for a wide class of parabolic systems with general growth
No full textWe prove the local boundedness of weak solutions for the following non-linear second order parabolic systems: (formula presented), |Du| where Ω ⊂ Rn is a bounded domain and φ is a given N-function. The proof of this result is based on a Moser-type iteration argument
Fractional p&q-Laplacian problems with potentials vanishing at infinity
No full textIn this paper we prove the existence of a positive and a negative ground state weak solution for the following class of fractional p&g-Laplacian problems
[formula]
where [formula]and [formula] are continuous, positive functions, allowed for vanishing behavior at infinity, ƒ is a continuous function with quasicritical growth and the leading operator [formula] , with t ∈ {p, q}, is the fractional t-Laplacian operator
Ground state solutions for a (p,q)-Choquard equation with a general nonlinearity
Full text linkIn this paper, we study the existence of ground state solutions for the following (p,q)-Choquard equation: −Δpu−Δqu+|u|p−2u+|u|q−2u=(Iα⁎F(u))f(u) in RN, where 2≤
The critical fractional Ambrosetti–Prodi problem
No full textIn this paper we focus on the following nonlocal problem with critical growth: {(-Δ)su=λu+u+2s∗-1+f(x)inΩ,u=0inRN\Ω,where s∈ (0 , 1) , N> 2 s, Ω ⊂ RN is a smooth bounded domain, λ> 0 , (- Δ) s is the fractional Laplacian, f= te1+ h where t∈ R, e1 is the first eigenfunction of (- Δ) s with homogeneous Dirichlet boundary datum, and h∈ L∞(Ω) is such that ∫Ωhe1dx=0. According to the interaction of the nonlinear term with the spectrum of (- Δ) s, we establish some existence and multiplicity results for the above problem by means of variational methods
A multiplicity result for a (p, q)-Schrödinger–Kirchhoff type equation
Full text linkIn this paper, we study a class of (p, q)-Schrödinger–Kirchhoff type equations involving a continuous positive potential satisfying del Pino–Felmer type conditions and a continuous nonlinearity with subcritical growth at infinity. By applying variational methods, penalization techniques and Lusternik–Schnirelman category theory, we relate the number of positive solutions with the topology of the set where the potential attains its minimum values
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